0132_0213_1230_3012
Counting sequence:
1, 1, 2, 6, 20, 63, 187, 552, 1680, 5342, 17689, 60425, 211017, 748448, 2684799, 9714433, 35395159, 129717292, 477780104, 1767540780, 6564668021, 24467351145, 91484715550, 343063893096, 1289912669420, 4861963389433, 18367386961292, 69533618558867, 263748086823120, 1002242486459683, 3814987041172117, 14544637116528338, 55534067030274658, 212336134716483188, 812944050754646943, 3116285512111385975, 11959798420259344811, 45950804393404537566, 176733862924548069869, 680425372005019377380, 2622127042826515936711, 10113918592737843366520, 39044429914104168745210, 150853479209484533208916, 583300119601794622569251, 2257117854094843230674411, 8740328711568362569838420, 33868773757261423409541618, 131327898242310115552825870, 509552245179898633396558247, 1978261657756723636528723314, 7684785670515442338454218125, 29869166945774877836223964202, 116157871455786937989765392313, 451959718027962478872716022323, 1759414616608836885756425018435, 6852456927844909526937964550086, 26700952856774923962795981287716, 104088460289122448150234403875689, 405944995127577273963524326345027, 1583850964596120619151577822518577, 6182127958584856803415142924937336, 24139737743045629131565077970416867, 94295850558771984399638571054577061, 368479169875816668702408857459031051, 1440418573150919687319278913524346376, 5632681584560312771887476576729258660, 22033725021956517537145646577926427368, 86218923998960285873759783645869090505, 337485502510215975851932006695933532885, 1321422108420282271080238486002948042378, 5175569924646105560599532621228011092984, 20276890389709399865290183114659009644520, 79463489365077377845930606226703993221613, 311496878311103321146981027901003048571384, 1221395654430378811847650193467380413807983, 4790408930363303911366165149202215947873124, 18793142726809884575286919157285793542765967, 73745243611532458459841267605515886236138049, 289450081175264899454586077522283486932788095, 1136359577947336271932237339975780561978236036, 4462290049988320482464450223424942665770858990, 17526585015616776834737558369715385538563844695, 68854441132780194707892887738206801156597076081, 270557451039395118028652134696145679594798437331, 1063353702922273835973056000857270184427539432006, 4180080073556524734514734513798235214340710232465, 16435314834665426797069222332017121459050778628798, 64633260585762914370496792228653972202410270901615, 254224158304000796523953750263856128478226474885320, 1000134600800354781929399869506569047166403288523998, 3935312233584004685417854810703400995314721703810724, 15487357822491889407128329439658441543048700797218575, 60960876535340415751462568532589837973925463497075743, 239993345518077005168915786526997088970031881542721264, 944973797977428207852605890261980309024458646472627638, 3721443204405954385563870580993328052143527838860871234, 14657929356129575437016877925885195494900288379002477427, 57743358069601357782187700766499181716774254991110181614, 227508830794229349661819540712601504586246876989537844305, 896519947090131496687170070707925933462324914480180584206
Generating function in Maple syntax:
1/4*(-2*(x-1/2)*(x^2+x-1)*(x-1)^5*(1-4*x)^(1/2)+6*x^9-10*x^8-9*x^7+14*x^6+10*x^5-37*x^4+43*x^3-26*x^2+8*x-1)/(x-1/2)/(x^2+x-1)/(x-1)^5/x
Generating function in latex syntax:
\frac{-2 \left(x -\frac{1}{2}\right) \left(x^{2}+x -1\right) \left(x -1\right)^{5} \sqrt{1-4 x}+6 x^{9}-10 x^{8}-9 x^{7}+14 x^{6}+10 x^{5}-37 x^{4}+43 x^{3}-26 x^{2}+8 x -1}{4 \left(x -\frac{1}{2}\right) \left(x^{2}+x -1\right) \left(x -1\right)^{5} x}
Generating function in sympy syntax:
(3*x**9/2 - 5*x**8/2 - 9*x**7/4 + 7*x**6/2 + 5*x**5/2 - 37*x**4/4 + 43*x**3/4 - 13*x**2/2 + 2*x + sqrt(1 - 4*x)*(1 - 2*x)*(x - 1)**5*(x**2 + x - 1)/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)*(6*x^9-10*x^8-9*x^7+14*x^6+10*x^5-37*x^4+43*x^3-26*x^2+8*x-1)*(x-1)^5*F(x)+9*x^17-26*x^16-39*x^15+225*x^14-244*x^13-280*x^12+1290*x^11-1975*x^10+1259*x^9+881*x^8-3010*x^7+3654*x^6-2767*x^5+1424*x^4-501*x^3+116*x^2-16*x+1 = 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(6 x^{9}-10 x^{8}-9 x^{7}+14 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)+9 x^{17}-26 x^{16}-39 x^{15}+225 x^{14}-244 x^{13}-280 x^{12}+1290 x^{11}-1975 x^{10}+1259 x^{9}+881 x^{8}-3010 x^{7}+3654 x^{6}-2767 x^{5}+1424 x^{4}-501 x^{3}+116 x^{2}-16 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 63
a(6) = 187
a(7) = 552
a(8) = 1680
a(9) = 5342
a(10) = 17689
a(11) = 60425
a(12) = 211017
a(13) = 748448
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+1846*n^2-3008*n-3600)/(n+8), n >= 14
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) = 63
a \! \left(6\right) = 187
a \! \left(7\right) = 552
a \! \left(8\right) = 1680
a \! \left(9\right) = 5342
a \! \left(10\right) = 17689
a \! \left(11\right) = 60425
a \! \left(12\right) = 211017
a \! \left(13\right) = 748448
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}+1846 n^{2}-3008 n -3600}{24 \left(n +8\right)}, \quad n \geq 14
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21192/
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[117,x]+F[4,x]
F[4,x] = F[12,x]*F[5,x]
F[5,x] = F[30,x]+F[6,x]
F[6,x] = F[16,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[15,x] = F[12,x]*F[8,x]
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[19,x]
F[19,x] = F[1,x]+F[17,x]
F[20,x] = F[21,x]
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[12,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = x^2
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[21,x]
F[28,x] = F[29,x]
F[29,x] = F[12,x]*F[27,x]
F[30,x] = F[31,x]+F[84,x]
F[31,x] = F[32,x]+F[43,x]
F[32,x] = F[33,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[11,x]+F[35,x]
F[35,x] = F[32,x]+F[36,x]
F[36,x] = F[37,x]+F[38,x]+F[42,x]
F[37,x] = 0
F[38,x] = F[12,x]*F[39,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[12,x]
F[41,x] = F[36,x]
F[42,x] = F[12,x]*F[32,x]
F[43,x] = F[37,x]+F[44,x]+F[67,x]
F[44,x] = F[12,x]*F[45,x]
F[45,x] = F[46,x]+F[52,x]
F[46,x] = F[47,x]+F[8,x]
F[47,x] = F[48,x]
F[48,x] = F[12,x]*F[49,x]
F[49,x] = F[50,x]+F[51,x]
F[50,x] = F[12,x]
F[51,x] = F[47,x]
F[52,x] = F[43,x]+F[53,x]
F[53,x] = 2*F[37,x]+F[54,x]+F[58,x]
F[54,x] = F[12,x]*F[55,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[47,x]
F[57,x] = F[53,x]
F[58,x] = F[12,x]*F[59,x]
F[59,x] = F[60,x]+F[66,x]
F[60,x] = F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[12,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[1,x]+F[63,x]
F[66,x] = F[58,x]
F[67,x] = F[12,x]*F[68,x]
F[68,x] = F[69,x]+F[73,x]
F[69,x] = F[63,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[12,x]*F[72,x]
F[72,x] = F[12,x]+F[70,x]
F[73,x] = F[74,x]+F[80,x]
F[74,x] = F[37,x]+F[67,x]+F[75,x]
F[75,x] = F[12,x]*F[76,x]
F[76,x] = F[63,x]+F[77,x]
F[77,x] = F[37,x]+F[75,x]+F[78,x]
F[78,x] = F[12,x]*F[79,x]
F[79,x] = F[63,x]+F[77,x]
F[80,x] = F[81,x]
F[81,x] = F[12,x]*F[82,x]
F[82,x] = F[61,x]+F[83,x]
F[83,x] = F[81,x]
F[84,x] = F[108,x]+F[85,x]
F[85,x] = F[106,x]+F[37,x]+F[86,x]
F[86,x] = F[12,x]*F[87,x]
F[87,x] = F[88,x]+F[91,x]
F[88,x] = F[17,x]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[12,x]*F[17,x]
F[91,x] = F[85,x]+F[92,x]
F[92,x] = 2*F[37,x]+F[93,x]+F[97,x]
F[93,x] = F[12,x]*F[94,x]
F[94,x] = F[95,x]+F[96,x]
F[95,x] = F[89,x]
F[96,x] = F[92,x]
F[97,x] = F[12,x]*F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[12,x]
F[100,x] = F[101,x]+F[88,x]
F[101,x] = F[102,x]+F[98,x]
F[102,x] = 2*F[37,x]+F[103,x]+F[97,x]
F[103,x] = F[104,x]*F[12,x]
F[104,x] = F[105,x]+F[95,x]
F[105,x] = F[102,x]
F[106,x] = F[107,x]*F[12,x]
F[107,x] = F[32,x]+F[98,x]
F[108,x] = 2*F[37,x]+F[109,x]+F[113,x]
F[109,x] = F[110,x]*F[12,x]
F[110,x] = F[111,x]+F[112,x]
F[111,x] = F[20,x]
F[112,x] = F[108,x]
F[113,x] = F[114,x]*F[12,x]
F[114,x] = F[115,x]+F[116,x]
F[115,x] = F[61,x]
F[116,x] = F[113,x]
F[117,x] = F[118,x]*F[12,x]
F[118,x] = F[1,x]+F[119,x]+F[145,x]+F[210,x]
F[119,x] = F[120,x,1]
F[120,x,k[0]] = F[121,x,k[0]]*F[122,x,k[0]]
F[121,x,k[0]] = k[0]*x
F[122,x,k[0]] = F[1,x]+F[120,x,k[0]]+F[123,x,k[0]]+F[125,x,k[0]]
F[123,x,k[0]] = F[12,x]*F[124,x,k[0]]
F[124,x,k[0]] = 1/(-1+k[0])*(F[122,x,k[0]]*k[0]-F[122,x,1])
F[125,x,k[0]] = F[12,x]*F[126,x,k[0]]
F[126,x,k[0]] = F[127,x]+F[128,x,k[0]]
F[127,x] = F[65,x]+F[79,x]
F[128,x,k[0]] = F[129,x,k[0]]+F[137,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]+F[133,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[121,x,k[0]]*F[132,x,k[0]]
F[132,x,k[0]] = F[1,x]+F[130,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]+F[136,x,k[0]]+F[37,x]
F[134,x,k[0]] = F[121,x,k[0]]*F[135,x,k[0]]
F[135,x,k[0]] = F[133,x,k[0]]+F[63,x]
F[136,x,k[0]] = F[12,x]*F[129,x,k[0]]
F[137,x,k[0]] = F[138,x,k[0]]+F[141,x,k[0]]
F[138,x,k[0]] = F[139,x,k[0]]
F[139,x,k[0]] = F[12,x]*F[140,x,k[0]]
F[140,x,k[0]] = F[130,x,k[0]]+F[138,x,k[0]]
F[141,x,k[0]] = 2*F[37,x]+F[142,x,k[0]]+F[144,x,k[0]]
F[142,x,k[0]] = F[12,x]*F[143,x,k[0]]
F[143,x,k[0]] = F[133,x,k[0]]+F[141,x,k[0]]
F[144,x,k[0]] = F[12,x]*F[137,x,k[0]]
F[145,x] = F[12,x]*F[146,x]
F[146,x] = F[1,x]+F[119,x]+F[147,x]+F[150,x]+F[209,x]
F[147,x] = F[148,x,1]
F[148,x,k[0]] = F[12,x]*F[149,x,k[0]]
F[149,x,k[0]] = 1/(-1+k[0])*(F[122,x,k[0]]*k[0]-F[122,x,1])
F[150,x] = F[151,x,1]
F[151,x,k[0]] = F[12,x]*F[152,x,k[0]]
F[152,x,k[0]] = (F[153,x,k[0]]*k[0]-F[153,x,1])/(-1+k[0])
F[153,x,k[0]] = F[1,x]+F[120,x,k[0]]+F[148,x,k[0]]+F[151,x,k[0]]+F[154,x,k[0]]
F[154,x,k[0]] = F[12,x]*F[155,x,k[0]]
F[155,x,k[0]] = F[126,x,k[0]]+F[156,x,k[0]]
F[156,x,k[0]] = F[157,x]+F[185,x,k[0]]
F[157,x] = F[158,x]+F[79,x]
F[158,x] = F[159,x]+F[165,x]
F[159,x] = F[160,x]+F[163,x]+F[37,x]
F[160,x] = F[12,x]*F[161,x]
F[161,x] = F[12,x]+F[162,x]
F[162,x] = F[160,x]+F[37,x]+F[62,x]
F[163,x] = F[12,x]*F[164,x]
F[164,x] = F[159,x]+F[63,x]
F[165,x] = F[166,x]+F[175,x]+F[177,x]+F[37,x]
F[166,x] = F[12,x]*F[167,x]
F[167,x] = F[168,x]+F[171,x]
F[168,x] = F[169,x]
F[169,x] = F[12,x]*F[170,x]
F[170,x] = F[12,x]+F[168,x]
F[171,x] = 2*F[37,x]+F[166,x]+F[172,x]
F[172,x] = F[12,x]*F[173,x]
F[173,x] = F[174,x]+F[61,x]
F[174,x] = F[172,x]
F[175,x] = F[12,x]*F[176,x]
F[176,x] = F[165,x]+F[77,x]
F[177,x] = F[12,x]*F[178,x]
F[178,x] = F[179,x]+F[182,x]
F[179,x] = F[180,x]
F[180,x] = F[12,x]*F[181,x]
F[181,x] = F[179,x]+F[63,x]
F[182,x] = 2*F[37,x]+F[177,x]+F[183,x]
F[183,x] = F[12,x]*F[184,x]
F[184,x] = F[182,x]+F[77,x]
F[185,x,k[0]] = F[186,x,k[0]]+F[194,x,k[0]]
F[186,x,k[0]] = F[187,x,k[0]]+F[190,x,k[0]]
F[187,x,k[0]] = F[188,x,k[0]]
F[188,x,k[0]] = F[121,x,k[0]]*F[189,x,k[0]]
F[189,x,k[0]] = F[187,x,k[0]]+F[63,x]
F[190,x,k[0]] = 2*F[37,x]+F[191,x,k[0]]+F[193,x,k[0]]
F[191,x,k[0]] = F[121,x,k[0]]*F[192,x,k[0]]
F[192,x,k[0]] = F[190,x,k[0]]+F[77,x]
F[193,x,k[0]] = F[12,x]*F[186,x,k[0]]
F[194,x,k[0]] = F[195,x,k[0]]+F[198,x,k[0]]
F[195,x,k[0]] = F[196,x,k[0]]
F[196,x,k[0]] = F[12,x]*F[197,x,k[0]]
F[197,x,k[0]] = F[187,x,k[0]]+F[195,x,k[0]]
F[198,x,k[0]] = 3*F[37,x]+F[199,x,k[0]]+F[201,x,k[0]]
F[199,x,k[0]] = F[12,x]*F[200,x,k[0]]
F[200,x,k[0]] = F[190,x,k[0]]+F[198,x,k[0]]
F[201,x,k[0]] = F[12,x]*F[202,x,k[0]]
F[202,x,k[0]] = F[203,x,k[0]]+F[206,x,k[0]]
F[203,x,k[0]] = F[204,x,k[0]]
F[204,x,k[0]] = F[12,x]*F[205,x,k[0]]
F[205,x,k[0]] = F[187,x,k[0]]+F[203,x,k[0]]
F[206,x,k[0]] = 3*F[37,x]+F[201,x,k[0]]+F[207,x,k[0]]
F[207,x,k[0]] = F[12,x]*F[208,x,k[0]]
F[208,x,k[0]] = F[190,x,k[0]]+F[206,x,k[0]]
F[209,x] = F[154,x,1]
F[210,x] = F[12,x]*F[211,x]
F[211,x] = F[127,x]+F[157,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_{117}\! \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_{30}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{16}\! \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_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = x^{2}
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{21}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{84}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{43}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)+F_{42}\! \left(x \right)
F_{37}\! \left(x \right) = 0
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right)
F_{41}\! \left(x \right) = F_{36}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{32}\! \left(x \right)
F_{43}\! \left(x \right) = F_{37}\! \left(x \right)+F_{44}\! \left(x \right)+F_{67}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{52}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{8}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \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 \right)+F_{51}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right)
F_{51}\! \left(x \right) = F_{47}\! \left(x \right)
F_{52}\! \left(x \right) = F_{43}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{54}\! \left(x \right)+F_{58}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{47}\! \left(x \right)
F_{57}\! \left(x \right) = F_{53}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{66}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{1}\! \left(x \right)+F_{63}\! \left(x \right)
F_{66}\! \left(x \right) = F_{58}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{73}\! \left(x \right)
F_{69}\! \left(x \right) = F_{63}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right)+F_{70}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{80}\! \left(x \right)
F_{74}\! \left(x \right) = F_{37}\! \left(x \right)+F_{67}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{63}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{37}\! \left(x \right)+F_{75}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{63}\! \left(x \right)+F_{77}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{61}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{81}\! \left(x \right)
F_{84}\! \left(x \right) = F_{108}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{106}\! \left(x \right)+F_{37}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{12}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{91}\! \left(x \right)
F_{88}\! \left(x \right) = F_{17}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{91}\! \left(x \right) = F_{85}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{93}\! \left(x \right)+F_{97}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{96}\! \left(x \right)
F_{95}\! \left(x \right) = F_{89}\! \left(x \right)
F_{96}\! \left(x \right) = F_{92}\! \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 \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{12}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{88}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{98}\! \left(x \right)
F_{102}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{103}\! \left(x \right)+F_{97}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{12}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{95}\! \left(x \right)
F_{105}\! \left(x \right) = F_{102}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{12}\! \left(x \right)
F_{107}\! \left(x \right) = F_{32}\! \left(x \right)+F_{98}\! \left(x \right)
F_{108}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{109}\! \left(x \right)+F_{113}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{12}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{112}\! \left(x \right)
F_{111}\! \left(x \right) = F_{20}\! \left(x \right)
F_{112}\! \left(x \right) = F_{108}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{12}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{116}\! \left(x \right)
F_{115}\! \left(x \right) = F_{61}\! \left(x \right)
F_{116}\! \left(x \right) = F_{113}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{12}\! \left(x \right)
F_{118}\! \left(x \right) = F_{1}\! \left(x \right)+F_{119}\! \left(x \right)+F_{145}\! \left(x \right)+F_{210}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x , 1\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{122}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = y x
F_{122}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{120}\! \left(x , y\right)+F_{123}\! \left(x , y\right)+F_{125}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = -\frac{-y F_{122}\! \left(x , y\right)+F_{122}\! \left(x , 1\right)}{-1+y}
F_{125}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{126}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x \right)+F_{128}\! \left(x , y\right)
F_{127}\! \left(x \right) = F_{65}\! \left(x \right)+F_{79}\! \left(x \right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{137}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{132}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{130}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{136}\! \left(x , y\right)+F_{37}\! \left(x \right)
F_{134}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{135}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{63}\! \left(x \right)
F_{136}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{129}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{140}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{138}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = 2 F_{37}\! \left(x \right)+F_{142}\! \left(x , y\right)+F_{144}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{143}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{137}\! \left(x , y\right)
F_{145}\! \left(x \right) = F_{12}\! \left(x \right) F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{1}\! \left(x \right)+F_{119}\! \left(x \right)+F_{147}\! \left(x \right)+F_{150}\! \left(x \right)+F_{209}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x , 1\right)
F_{148}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{149}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = -\frac{-y F_{122}\! \left(x , y\right)+F_{122}\! \left(x , 1\right)}{-1+y}
F_{150}\! \left(x \right) = F_{151}\! \left(x , 1\right)
F_{151}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = -\frac{-y F_{153}\! \left(x , y\right)+F_{153}\! \left(x , 1\right)}{-1+y}
F_{153}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{120}\! \left(x , y\right)+F_{148}\! \left(x , y\right)+F_{151}\! \left(x , y\right)+F_{154}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{155}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{156}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x \right)+F_{185}\! \left(x , y\right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{79}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{165}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{163}\! \left(x \right)+F_{37}\! \left(x \right)
F_{160}\! \left(x \right) = F_{12}\! \left(x \right) F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{12}\! \left(x \right)+F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{160}\! \left(x \right)+F_{37}\! \left(x \right)+F_{62}\! \left(x \right)
F_{163}\! \left(x \right) = F_{12}\! \left(x \right) F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{159}\! \left(x \right)+F_{63}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)+F_{175}\! \left(x \right)+F_{177}\! \left(x \right)+F_{37}\! \left(x \right)
F_{166}\! \left(x \right) = F_{12}\! \left(x \right) F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)+F_{171}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{12}\! \left(x \right) F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{12}\! \left(x \right)+F_{168}\! \left(x \right)
F_{171}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{166}\! \left(x \right)+F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = F_{12}\! \left(x \right) F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)+F_{61}\! \left(x \right)
F_{174}\! \left(x \right) = F_{172}\! \left(x \right)
F_{175}\! \left(x \right) = F_{12}\! \left(x \right) F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{165}\! \left(x \right)+F_{77}\! \left(x \right)
F_{177}\! \left(x \right) = F_{12}\! \left(x \right) F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)+F_{182}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{12}\! \left(x \right) F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{179}\! \left(x \right)+F_{63}\! \left(x \right)
F_{182}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{177}\! \left(x \right)+F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{12}\! \left(x \right) F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{182}\! \left(x \right)+F_{77}\! \left(x \right)
F_{185}\! \left(x , y\right) = F_{186}\! \left(x , y\right)+F_{194}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right)+F_{190}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{188}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{189}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{187}\! \left(x , y\right)+F_{63}\! \left(x \right)
F_{190}\! \left(x , y\right) = 2 F_{37}\! \left(x \right)+F_{191}\! \left(x , y\right)+F_{193}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{192}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{190}\! \left(x , y\right)+F_{77}\! \left(x \right)
F_{193}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{186}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right)+F_{198}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{197}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{187}\! \left(x , y\right)+F_{195}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = 3 F_{37}\! \left(x \right)+F_{199}\! \left(x , y\right)+F_{201}\! \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_{190}\! \left(x , y\right)+F_{198}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{202}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{206}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{204}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{205}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{187}\! \left(x , y\right)+F_{203}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = 3 F_{37}\! \left(x \right)+F_{201}\! \left(x , y\right)+F_{207}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{208}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{190}\! \left(x , y\right)+F_{206}\! \left(x , y\right)
F_{209}\! \left(x \right) = F_{154}\! \left(x , 1\right)
F_{210}\! \left(x \right) = F_{12}\! \left(x \right) F_{211}\! \left(x \right)
F_{211}\! \left(x \right) = F_{127}\! \left(x \right)+F_{157}\! \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_117(x) + F_4(x))
Eq(F_4(x), F_12(x)*F_5(x))
Eq(F_5(x), F_30(x) + F_6(x))
Eq(F_6(x), F_16(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))
Eq(F_15(x), F_12(x)*F_8(x))
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_12(x)*F_19(x))
Eq(F_19(x), F_1(x) + F_17(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_12(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_26(x))
Eq(F_23(x), F_12(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), x**2)
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_21(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_12(x)*F_27(x))
Eq(F_30(x), F_31(x) + F_84(x))
Eq(F_31(x), F_32(x) + F_43(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_11(x) + F_35(x))
Eq(F_35(x), F_32(x) + F_36(x))
Eq(F_36(x), F_37(x) + F_38(x) + F_42(x))
Eq(F_37(x), 0)
Eq(F_38(x), F_12(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_12(x))
Eq(F_41(x), F_36(x))
Eq(F_42(x), F_12(x)*F_32(x))
Eq(F_43(x), F_37(x) + F_44(x) + F_67(x))
Eq(F_44(x), F_12(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_52(x))
Eq(F_46(x), F_47(x) + F_8(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_12(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_51(x))
Eq(F_50(x), F_12(x))
Eq(F_51(x), F_47(x))
Eq(F_52(x), F_43(x) + F_53(x))
Eq(F_53(x), 2*F_37(x) + F_54(x) + F_58(x))
Eq(F_54(x), F_12(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_47(x))
Eq(F_57(x), F_53(x))
Eq(F_58(x), F_12(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_66(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_12(x)*F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_1(x) + F_63(x))
Eq(F_66(x), F_58(x))
Eq(F_67(x), F_12(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_73(x))
Eq(F_69(x), F_63(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_12(x)*F_72(x))
Eq(F_72(x), F_12(x) + F_70(x))
Eq(F_73(x), F_74(x) + F_80(x))
Eq(F_74(x), F_37(x) + F_67(x) + F_75(x))
Eq(F_75(x), F_12(x)*F_76(x))
Eq(F_76(x), F_63(x) + F_77(x))
Eq(F_77(x), F_37(x) + F_75(x) + F_78(x))
Eq(F_78(x), F_12(x)*F_79(x))
Eq(F_79(x), F_63(x) + F_77(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_12(x)*F_82(x))
Eq(F_82(x), F_61(x) + F_83(x))
Eq(F_83(x), F_81(x))
Eq(F_84(x), F_108(x) + F_85(x))
Eq(F_85(x), F_106(x) + F_37(x) + F_86(x))
Eq(F_86(x), F_12(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_91(x))
Eq(F_88(x), F_17(x) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_12(x)*F_17(x))
Eq(F_91(x), F_85(x) + F_92(x))
Eq(F_92(x), 2*F_37(x) + F_93(x) + F_97(x))
Eq(F_93(x), F_12(x)*F_94(x))
Eq(F_94(x), F_95(x) + F_96(x))
Eq(F_95(x), F_89(x))
Eq(F_96(x), F_92(x))
Eq(F_97(x), F_12(x)*F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_12(x))
Eq(F_100(x), F_101(x) + F_88(x))
Eq(F_101(x), F_102(x) + F_98(x))
Eq(F_102(x), F_103(x) + 2*F_37(x) + F_97(x))
Eq(F_103(x), F_104(x)*F_12(x))
Eq(F_104(x), F_105(x) + F_95(x))
Eq(F_105(x), F_102(x))
Eq(F_106(x), F_107(x)*F_12(x))
Eq(F_107(x), F_32(x) + F_98(x))
Eq(F_108(x), F_109(x) + F_113(x) + 2*F_37(x))
Eq(F_109(x), F_110(x)*F_12(x))
Eq(F_110(x), F_111(x) + F_112(x))
Eq(F_111(x), F_20(x))
Eq(F_112(x), F_108(x))
Eq(F_113(x), F_114(x)*F_12(x))
Eq(F_114(x), F_115(x) + F_116(x))
Eq(F_115(x), F_61(x))
Eq(F_116(x), F_113(x))
Eq(F_117(x), F_118(x)*F_12(x))
Eq(F_118(x), F_1(x) + F_119(x) + F_145(x) + F_210(x))
Eq(F_119(x), F_120(x, 1))
Eq(F_120(x, k_0), F_121(x, k_0)*F_122(x, k_0))
Eq(F_121(x, k_0), k_0*x)
Eq(F_122(x, k_0), F_1(x) + F_120(x, k_0) + F_123(x, k_0) + F_125(x, k_0))
Eq(F_123(x, k_0), F_12(x)*F_124(x, k_0))
Eq(F_124(x, k_0), (-k_0*F_122(x, k_0) + F_122(x, 1))/(1 - k_0))
Eq(F_125(x, k_0), F_12(x)*F_126(x, k_0))
Eq(F_126(x, k_0), F_127(x) + F_128(x, k_0))
Eq(F_127(x), F_65(x) + F_79(x))
Eq(F_128(x, k_0), F_129(x, k_0) + F_137(x, k_0))
Eq(F_129(x, k_0), F_130(x, k_0) + F_133(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_121(x, k_0)*F_132(x, k_0))
Eq(F_132(x, k_0), F_1(x) + F_130(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0) + F_136(x, k_0) + F_37(x))
Eq(F_134(x, k_0), F_121(x, k_0)*F_135(x, k_0))
Eq(F_135(x, k_0), F_133(x, k_0) + F_63(x))
Eq(F_136(x, k_0), F_12(x)*F_129(x, k_0))
Eq(F_137(x, k_0), F_138(x, k_0) + F_141(x, k_0))
Eq(F_138(x, k_0), F_139(x, k_0))
Eq(F_139(x, k_0), F_12(x)*F_140(x, k_0))
Eq(F_140(x, k_0), F_130(x, k_0) + F_138(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0) + F_144(x, k_0) + 2*F_37(x))
Eq(F_142(x, k_0), F_12(x)*F_143(x, k_0))
Eq(F_143(x, k_0), F_133(x, k_0) + F_141(x, k_0))
Eq(F_144(x, k_0), F_12(x)*F_137(x, k_0))
Eq(F_145(x), F_12(x)*F_146(x))
Eq(F_146(x), F_1(x) + F_119(x) + F_147(x) + F_150(x) + F_209(x))
Eq(F_147(x), F_148(x, 1))
Eq(F_148(x, k_0), F_12(x)*F_149(x, k_0))
Eq(F_149(x, k_0), (k_0*F_122(x, k_0) - F_122(x, 1))/(k_0 - 1))
Eq(F_150(x), F_151(x, 1))
Eq(F_151(x, k_0), F_12(x)*F_152(x, k_0))
Eq(F_152(x, k_0), (-k_0*F_153(x, k_0) + F_153(x, 1))/(1 - k_0))
Eq(F_153(x, k_0), F_1(x) + F_120(x, k_0) + F_148(x, k_0) + F_151(x, k_0) + F_154(x, k_0))
Eq(F_154(x, k_0), F_12(x)*F_155(x, k_0))
Eq(F_155(x, k_0), F_126(x, k_0) + F_156(x, k_0))
Eq(F_156(x, k_0), F_157(x) + F_185(x, k_0))
Eq(F_157(x), F_158(x) + F_79(x))
Eq(F_158(x), F_159(x) + F_165(x))
Eq(F_159(x), F_160(x) + F_163(x) + F_37(x))
Eq(F_160(x), F_12(x)*F_161(x))
Eq(F_161(x), F_12(x) + F_162(x))
Eq(F_162(x), F_160(x) + F_37(x) + F_62(x))
Eq(F_163(x), F_12(x)*F_164(x))
Eq(F_164(x), F_159(x) + F_63(x))
Eq(F_165(x), F_166(x) + F_175(x) + F_177(x) + F_37(x))
Eq(F_166(x), F_12(x)*F_167(x))
Eq(F_167(x), F_168(x) + F_171(x))
Eq(F_168(x), F_169(x))
Eq(F_169(x), F_12(x)*F_170(x))
Eq(F_170(x), F_12(x) + F_168(x))
Eq(F_171(x), F_166(x) + F_172(x) + 2*F_37(x))
Eq(F_172(x), F_12(x)*F_173(x))
Eq(F_173(x), F_174(x) + F_61(x))
Eq(F_174(x), F_172(x))
Eq(F_175(x), F_12(x)*F_176(x))
Eq(F_176(x), F_165(x) + F_77(x))
Eq(F_177(x), F_12(x)*F_178(x))
Eq(F_178(x), F_179(x) + F_182(x))
Eq(F_179(x), F_180(x))
Eq(F_180(x), F_12(x)*F_181(x))
Eq(F_181(x), F_179(x) + F_63(x))
Eq(F_182(x), F_177(x) + F_183(x) + 2*F_37(x))
Eq(F_183(x), F_12(x)*F_184(x))
Eq(F_184(x), F_182(x) + F_77(x))
Eq(F_185(x, k_0), F_186(x, k_0) + F_194(x, k_0))
Eq(F_186(x, k_0), F_187(x, k_0) + F_190(x, k_0))
Eq(F_187(x, k_0), F_188(x, k_0))
Eq(F_188(x, k_0), F_121(x, k_0)*F_189(x, k_0))
Eq(F_189(x, k_0), F_187(x, k_0) + F_63(x))
Eq(F_190(x, k_0), F_191(x, k_0) + F_193(x, k_0) + 2*F_37(x))
Eq(F_191(x, k_0), F_121(x, k_0)*F_192(x, k_0))
Eq(F_192(x, k_0), F_190(x, k_0) + F_77(x))
Eq(F_193(x, k_0), F_12(x)*F_186(x, k_0))
Eq(F_194(x, k_0), F_195(x, k_0) + F_198(x, k_0))
Eq(F_195(x, k_0), F_196(x, k_0))
Eq(F_196(x, k_0), F_12(x)*F_197(x, k_0))
Eq(F_197(x, k_0), F_187(x, k_0) + F_195(x, k_0))
Eq(F_198(x, k_0), F_199(x, k_0) + F_201(x, k_0) + 3*F_37(x))
Eq(F_199(x, k_0), F_12(x)*F_200(x, k_0))
Eq(F_200(x, k_0), F_190(x, k_0) + F_198(x, k_0))
Eq(F_201(x, k_0), F_12(x)*F_202(x, k_0))
Eq(F_202(x, k_0), F_203(x, k_0) + F_206(x, k_0))
Eq(F_203(x, k_0), F_204(x, k_0))
Eq(F_204(x, k_0), F_12(x)*F_205(x, k_0))
Eq(F_205(x, k_0), F_187(x, k_0) + F_203(x, k_0))
Eq(F_206(x, k_0), F_201(x, k_0) + F_207(x, k_0) + 3*F_37(x))
Eq(F_207(x, k_0), F_12(x)*F_208(x, k_0))
Eq(F_208(x, k_0), F_190(x, k_0) + F_206(x, k_0))
Eq(F_209(x), F_154(x, 1))
Eq(F_210(x), F_12(x)*F_211(x))
Eq(F_211(x), F_127(x) + F_157(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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "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], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": []}, 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