0123_0132_0213_1230_3012
Counting sequence:
1, 1, 2, 6, 19, 59, 176, 526, 1623, 5222, 17442, 59923, 210004, 746412, 2680716, 9706255, 35378790, 129684540, 477714585, 1767409726, 6564405896, 24466826877, 91483666995, 343061795966, 1289908475139, 4861955000849, 18367370184101, 69533585004461, 263748019714283, 1002242352241983, 3814986772736690, 14544636579657456, 55534065956532865, 212336132568999572, 812944046459679680, 3116285503521451417, 11959798403079475662, 45950804359044799234, 176733862855828593170, 680425371867580423946, 2622127042551638029806, 10113918592188087552672, 39044429913004657117475, 150853479207285509953406, 583300119597396576058190, 2257117854086047137652247, 8740328711550770383794049, 33868773757226239037452832, 131327898242239746808648253, 509552245179757895908202967, 1978261657756442161552012707, 7684785670514879388500796863, 29869166945773751936317121629, 116157871455784686189951707117, 451959718027957975273088651880, 1759414616608827878557170277497, 6852456927844891512539455068157, 26700952856774887933998962323804, 104088460289122376092640365947810, 405944995127577129848336250489213, 1583850964596120330921201670806892, 6182127958584856226954390621513908, 24139737743045627978643573363569952, 94295850558771982093795561840883171, 368479169875816664090722839031643210, 1440418573150919678095906876669570632, 5632681584560312753440732503019707109, 22033725021956517500252158430507324202, 86218923998960285799972807351030884108, 337485502510215975704358054106257120025, 1321422108420282270785090580823595216591, 5175569924646105560009236810869305441342, 20276890389709399864109591493941598341167, 79463489365077377843569422985269170614837, 311496878311103321142258661418133403357761, 1221395654430378811838205460501641123380665, 4790408930363303911347275683270737367018415, 18793142726809884575249140225422836381056475, 73745243611532458459765709741789971912718990, 289450081175264899454434961794831658285949901, 1136359577947336271931935108520876904684559571, 4462290049988320482463845760515135351183505982, 17526585015616776834736349443895770909389138600, 68854441132780194707890469886567571898247663811, 270557451039395118028647298992867221078099612710, 1063353702922273835973046329450713267394141782682, 4180080073556524734514715170985121380273914933734, 16435314834665426797069183646390893790917188031252, 64633260585762914370496714857401516866143089706438, 254224158304000796523953595521351217805692112494880, 1000134600800354781929399560021559225821334563743031, 3935312233584004685417854191733381352624584254248702, 15487357822491889407128328201718402257668425898094442, 60960876535340415751462566056709759403164913698827387, 239993345518077005168915781575236931828510781946224461, 944973797977428207852605880358459994741416447279633940, 3721443204405954385563870561186287423577443440474883745, 14657929356129575437016877886271114237768119582230502355, 57743358069601357782187700687271019202509917397566231375, 227508830794229349661819540554145179557718201802449943731, 896519947090131496687170070391013283405267564106004782961
Generating function in Maple syntax:
1/4*(-2*(x-1)^5*(x-1/2)*(x^2+x-1)*(1-4*x)^(1/2)+2*x^10+2*x^9-12*x^8+x^7+6*x^6+12*x^5-37*x^4+43*x^3-26*x^2+8*x-1)/(x-1)^5/x/(x-1/2)/(x^2+x-1)
Generating function in latex syntax:
\frac{-2 \left(x -1\right)^{5} \left(x -\frac{1}{2}\right) \left(x^{2}+x -1\right) \sqrt{1-4 x}+2 x^{10}+2 x^{9}-12 x^{8}+x^{7}+6 x^{6}+12 x^{5}-37 x^{4}+43 x^{3}-26 x^{2}+8 x -1}{4 \left(x -1\right)^{5} x \left(x -\frac{1}{2}\right) \left(x^{2}+x -1\right)}
Generating function in sympy syntax:
(x**10/2 + x**9/2 - 3*x**8 + x**7/4 + 3*x**6/2 + 3*x**5 - 37*x**4/4 + 43*x**3/4 - 13*x**2/2 + 2*x - sqrt(1 - 4*x)*(x - 1)**5*(x - 1/2)*(x**2 + x - 1)/2 - 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)*(2*x^10+2*x^9-12*x^8+x^7+6*x^6+12*x^5-37*x^4+43*x^3-26*x^2+8*x-1)*(x-1)^5*F(x)+x^19+2*x^18-11*x^17-7*x^16+6*x^15+150*x^14-285*x^13-119*x^12+1226*x^11-2177*x^10+1642*x^9+536*x^8-2822*x^7+3591*x^6-2755*x^5+1423*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(2 x^{10}+2 x^{9}-12 x^{8}+x^{7}+6 x^{6}+12 x^{5}-37 x^{4}+43 x^{3}-26 x^{2}+8 x -1\right) \left(x -1\right)^{5} F \! \left(x \right)+x^{19}+2 x^{18}-11 x^{17}-7 x^{16}+6 x^{15}+150 x^{14}-285 x^{13}-119 x^{12}+1226 x^{11}-2177 x^{10}+1642 x^{9}+536 x^{8}-2822 x^{7}+3591 x^{6}-2755 x^{5}+1423 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) = 19
a(5) = 59
a(6) = 176
a(7) = 526
a(8) = 1623
a(9) = 5222
a(10) = 17442
a(11) = 59923
a(12) = 210004
a(13) = 746412
a(14) = 2680716
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+1918*n^2-3680*n-2976)/(n+8), n >= 15
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) = 19
a \! \left(5\right) = 59
a \! \left(6\right) = 176
a \! \left(7\right) = 526
a \! \left(8\right) = 1623
a \! \left(9\right) = 5222
a \! \left(10\right) = 17442
a \! \left(11\right) = 59923
a \! \left(12\right) = 210004
a \! \left(13\right) = 746412
a \! \left(14\right) = 2680716
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}+1918 n^{2}-3680 n -2976}{24 \left(n +8\right)}, \quad n \geq 15
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21489/
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[91,x]
F[4,x] = F[12,x]*F[5,x]
F[5,x] = F[27,x]+F[6,x]
F[6,x] = F[17,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[14,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x,1]
F[13,x,k[0]] = k[0]*x
F[14,x] = F[15,x]+F[8,x]
F[15,x] = F[16,x]
F[16,x] = F[12,x]*F[8,x]
F[17,x] = F[12,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[21,x]+F[24,x]
F[21,x] = F[12,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = x^2
F[24,x] = F[18,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[12,x]*F[18,x]
F[27,x] = F[28,x]+F[81,x]
F[28,x] = F[29,x]+F[40,x]
F[29,x] = F[30,x]
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[11,x]+F[32,x]
F[32,x] = F[29,x]+F[33,x]
F[33,x] = F[34,x]+F[35,x]+F[39,x]
F[34,x] = 0
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[12,x]
F[38,x] = F[33,x]
F[39,x] = F[12,x]*F[29,x]
F[40,x] = F[34,x]+F[41,x]+F[64,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[43,x]+F[49,x]
F[43,x] = F[44,x]+F[8,x]
F[44,x] = F[45,x]
F[45,x] = F[12,x]*F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[12,x]
F[48,x] = F[44,x]
F[49,x] = F[40,x]+F[50,x]
F[50,x] = 2*F[34,x]+F[51,x]+F[55,x]
F[51,x] = F[12,x]*F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = F[44,x]
F[54,x] = F[50,x]
F[55,x] = F[12,x]*F[56,x]
F[56,x] = F[57,x]+F[63,x]
F[57,x] = F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[1,x]+F[60,x]
F[63,x] = F[55,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[66,x]+F[70,x]
F[66,x] = F[60,x]+F[67,x]
F[67,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[77,x]
F[71,x] = F[34,x]+F[64,x]+F[72,x]
F[72,x] = F[12,x]*F[73,x]
F[73,x] = F[60,x]+F[74,x]
F[74,x] = F[34,x]+F[72,x]+F[75,x]
F[75,x] = F[12,x]*F[76,x]
F[76,x] = F[60,x]+F[74,x]
F[77,x] = F[78,x]
F[78,x] = F[12,x]*F[79,x]
F[79,x] = F[58,x]+F[80,x]
F[80,x] = F[78,x]
F[81,x] = F[33,x]+F[82,x]
F[82,x] = 2*F[34,x]+F[83,x]+F[87,x]
F[83,x] = F[12,x]*F[84,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[18,x]
F[86,x] = F[82,x]
F[87,x] = F[12,x]*F[88,x]
F[88,x] = F[89,x]+F[90,x]
F[89,x] = F[58,x]
F[90,x] = F[87,x]
F[91,x] = F[12,x]*F[92,x]
F[92,x] = F[1,x]+F[118,x]+F[180,x]+F[93,x]
F[93,x] = F[94,x,1]
F[94,x,k[0]] = F[13,x,k[0]]*F[95,x,k[0]]
F[95,x,k[0]] = F[1,x]+F[94,x,k[0]]+F[96,x,k[0]]+F[98,x,k[0]]
F[96,x,k[0]] = F[12,x]*F[97,x,k[0]]
F[97,x,k[0]] = 1/(-1+k[0])*(F[95,x,k[0]]*k[0]-F[95,x,1])
F[98,x,k[0]] = F[12,x]*F[99,x,k[0]]
F[99,x,k[0]] = F[100,x]+F[101,x,k[0]]
F[100,x] = F[62,x]+F[76,x]
F[101,x,k[0]] = F[102,x,k[0]]+F[110,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]+F[106,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]*F[13,x,k[0]]
F[105,x,k[0]] = F[1,x]+F[103,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]+F[109,x,k[0]]+F[34,x]
F[107,x,k[0]] = F[108,x,k[0]]*F[13,x,k[0]]
F[108,x,k[0]] = F[106,x,k[0]]+F[60,x]
F[109,x,k[0]] = F[102,x,k[0]]*F[12,x]
F[110,x,k[0]] = F[111,x,k[0]]+F[114,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]*F[12,x]
F[113,x,k[0]] = F[103,x,k[0]]+F[111,x,k[0]]
F[114,x,k[0]] = 2*F[34,x]+F[115,x,k[0]]+F[117,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]*F[12,x]
F[116,x,k[0]] = F[106,x,k[0]]+F[114,x,k[0]]
F[117,x,k[0]] = F[110,x,k[0]]*F[12,x]
F[118,x] = F[119,x]*F[12,x]
F[119,x] = F[120,x,1]
F[120,x,k[0]] = F[1,x]+F[121,x,k[0]]+F[123,x,k[0]]+F[125,x,k[0]]+F[94,x,k[0]]
F[121,x,k[0]] = F[12,x]*F[122,x,k[0]]
F[122,x,k[0]] = 1/(-1+k[0])*(F[95,x,k[0]]*k[0]-F[95,x,1])
F[123,x,k[0]] = F[12,x]*F[124,x,k[0]]
F[124,x,k[0]] = (F[120,x,k[0]]*k[0]-F[120,x,1])/(-1+k[0])
F[125,x,k[0]] = F[12,x]*F[126,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]+F[99,x,k[0]]
F[127,x,k[0]] = F[128,x]+F[156,x,k[0]]
F[128,x] = F[129,x]+F[76,x]
F[129,x] = F[130,x]+F[136,x]
F[130,x] = F[131,x]+F[134,x]+F[34,x]
F[131,x] = F[12,x]*F[132,x]
F[132,x] = F[12,x]+F[133,x]
F[133,x] = F[131,x]+F[34,x]+F[59,x]
F[134,x] = F[12,x]*F[135,x]
F[135,x] = F[130,x]+F[60,x]
F[136,x] = F[137,x]+F[146,x]+F[148,x]+F[34,x]
F[137,x] = F[12,x]*F[138,x]
F[138,x] = F[139,x]+F[142,x]
F[139,x] = F[140,x]
F[140,x] = F[12,x]*F[141,x]
F[141,x] = F[12,x]+F[139,x]
F[142,x] = 2*F[34,x]+F[137,x]+F[143,x]
F[143,x] = F[12,x]*F[144,x]
F[144,x] = F[145,x]+F[58,x]
F[145,x] = F[143,x]
F[146,x] = F[12,x]*F[147,x]
F[147,x] = F[136,x]+F[74,x]
F[148,x] = F[12,x]*F[149,x]
F[149,x] = F[150,x]+F[153,x]
F[150,x] = F[151,x]
F[151,x] = F[12,x]*F[152,x]
F[152,x] = F[150,x]+F[60,x]
F[153,x] = 2*F[34,x]+F[148,x]+F[154,x]
F[154,x] = F[12,x]*F[155,x]
F[155,x] = F[153,x]+F[74,x]
F[156,x,k[0]] = F[157,x,k[0]]+F[165,x,k[0]]
F[157,x,k[0]] = F[158,x,k[0]]+F[161,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]
F[159,x,k[0]] = F[13,x,k[0]]*F[160,x,k[0]]
F[160,x,k[0]] = F[158,x,k[0]]+F[60,x]
F[161,x,k[0]] = 2*F[34,x]+F[162,x,k[0]]+F[164,x,k[0]]
F[162,x,k[0]] = F[13,x,k[0]]*F[163,x,k[0]]
F[163,x,k[0]] = F[161,x,k[0]]+F[74,x]
F[164,x,k[0]] = F[12,x]*F[157,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]+F[169,x,k[0]]
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[158,x,k[0]]+F[166,x,k[0]]
F[169,x,k[0]] = 3*F[34,x]+F[170,x,k[0]]+F[172,x,k[0]]
F[170,x,k[0]] = F[12,x]*F[171,x,k[0]]
F[171,x,k[0]] = F[161,x,k[0]]+F[169,x,k[0]]
F[172,x,k[0]] = F[12,x]*F[173,x,k[0]]
F[173,x,k[0]] = F[174,x,k[0]]+F[177,x,k[0]]
F[174,x,k[0]] = F[175,x,k[0]]
F[175,x,k[0]] = F[12,x]*F[176,x,k[0]]
F[176,x,k[0]] = F[158,x,k[0]]+F[174,x,k[0]]
F[177,x,k[0]] = 3*F[34,x]+F[172,x,k[0]]+F[178,x,k[0]]
F[178,x,k[0]] = F[12,x]*F[179,x,k[0]]
F[179,x,k[0]] = F[161,x,k[0]]+F[177,x,k[0]]
F[180,x] = F[12,x]*F[181,x]
F[181,x] = F[100,x]+F[128,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_{4}\! \left(x \right)+F_{91}\! \left(x \right)
F_{4}\! \left(x \right) = F_{12}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{27}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{17}\! \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_{14}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{13}\! \left(x , y\right) = y x
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{8}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{17}\! \left(x \right) = F_{12}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{24}\! \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_{23}\! \left(x \right) = x^{2}
F_{24}\! \left(x \right) = F_{18}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{81}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{40}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{11}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{29}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)+F_{39}\! \left(x \right)
F_{34}\! \left(x \right) = 0
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right)
F_{38}\! \left(x \right) = F_{33}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{40}\! \left(x \right) = F_{34}\! \left(x \right)+F_{41}\! \left(x \right)+F_{64}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{49}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{8}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right)
F_{48}\! \left(x \right) = F_{44}\! \left(x \right)
F_{49}\! \left(x \right) = F_{40}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{51}\! \left(x \right)+F_{55}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{44}\! \left(x \right)
F_{54}\! \left(x \right) = F_{50}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{63}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \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_{1}\! \left(x \right)+F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{55}\! \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_{60}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \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_{77}\! \left(x \right)
F_{71}\! \left(x \right) = F_{34}\! \left(x \right)+F_{64}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{60}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{34}\! \left(x \right)+F_{72}\! \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_{60}\! \left(x \right)+F_{74}\! \left(x \right)
F_{77}\! \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_{58}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{78}\! \left(x \right)
F_{81}\! \left(x \right) = F_{33}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{83}\! \left(x \right)+F_{87}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{86}\! \left(x \right)
F_{85}\! \left(x \right) = F_{18}\! \left(x \right)
F_{86}\! \left(x \right) = F_{82}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{58}\! \left(x \right)
F_{90}\! \left(x \right) = F_{87}\! \left(x \right)
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{1}\! \left(x \right)+F_{118}\! \left(x \right)+F_{180}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x , 1\right)
F_{94}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{94}\! \left(x , y\right)+F_{96}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = -\frac{-y F_{95}\! \left(x , y\right)+F_{95}\! \left(x , 1\right)}{-1+y}
F_{98}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x \right)+F_{101}\! \left(x , y\right)
F_{100}\! \left(x \right) = F_{62}\! \left(x \right)+F_{76}\! \left(x \right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{110}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{106}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{13}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{103}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{109}\! \left(x , y\right)+F_{34}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{13}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{60}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{114}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{111}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = 2 F_{34}\! \left(x \right)+F_{115}\! \left(x , y\right)+F_{117}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{116}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{114}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{12}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x , 1\right)
F_{120}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{121}\! \left(x , y\right)+F_{123}\! \left(x , y\right)+F_{125}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{122}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = -\frac{-y F_{95}\! \left(x , y\right)+F_{95}\! \left(x , 1\right)}{-1+y}
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_{120}\! \left(x , y\right)+F_{120}\! \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 , y\right)+F_{99}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x \right)+F_{156}\! \left(x , y\right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{76}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{136}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{134}\! \left(x \right)+F_{34}\! \left(x \right)
F_{131}\! \left(x \right) = F_{12}\! \left(x \right) F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{12}\! \left(x \right)+F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{131}\! \left(x \right)+F_{34}\! \left(x \right)+F_{59}\! \left(x \right)
F_{134}\! \left(x \right) = F_{12}\! \left(x \right) F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{130}\! \left(x \right)+F_{60}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{146}\! \left(x \right)+F_{148}\! \left(x \right)+F_{34}\! \left(x \right)
F_{137}\! \left(x \right) = F_{12}\! \left(x \right) F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{142}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{12}\! \left(x \right) F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{12}\! \left(x \right)+F_{139}\! \left(x \right)
F_{142}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{137}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{12}\! \left(x \right) F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{58}\! \left(x \right)
F_{145}\! \left(x \right) = F_{143}\! \left(x \right)
F_{146}\! \left(x \right) = F_{12}\! \left(x \right) F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{136}\! \left(x \right)+F_{74}\! \left(x \right)
F_{148}\! \left(x \right) = F_{12}\! \left(x \right) F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{153}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{12}\! \left(x \right) F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{150}\! \left(x \right)+F_{60}\! \left(x \right)
F_{153}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{148}\! \left(x \right)+F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{12}\! \left(x \right) F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{153}\! \left(x \right)+F_{74}\! \left(x \right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{165}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{161}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{160}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{60}\! \left(x \right)
F_{161}\! \left(x , y\right) = 2 F_{34}\! \left(x \right)+F_{162}\! \left(x , y\right)+F_{164}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{74}\! \left(x \right)
F_{164}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{157}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{169}\! \left(x , y\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_{158}\! \left(x , y\right)+F_{166}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = 3 F_{34}\! \left(x \right)+F_{170}\! \left(x , y\right)+F_{172}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{171}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{169}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{173}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{177}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{176}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{174}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = 3 F_{34}\! \left(x \right)+F_{172}\! \left(x , y\right)+F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{179}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{177}\! \left(x , y\right)
F_{180}\! \left(x \right) = F_{12}\! \left(x \right) F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{100}\! \left(x \right)+F_{128}\! \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_4(x) + F_91(x))
Eq(F_4(x), F_12(x)*F_5(x))
Eq(F_5(x), F_27(x) + F_6(x))
Eq(F_6(x), F_17(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_14(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x, 1))
Eq(F_13(x, k_0), k_0*x)
Eq(F_14(x), F_15(x) + F_8(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_12(x)*F_8(x))
Eq(F_17(x), F_12(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_21(x) + F_24(x))
Eq(F_21(x), F_12(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), x**2)
Eq(F_24(x), F_18(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_12(x)*F_18(x))
Eq(F_27(x), F_28(x) + F_81(x))
Eq(F_28(x), F_29(x) + F_40(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_11(x) + F_32(x))
Eq(F_32(x), F_29(x) + F_33(x))
Eq(F_33(x), F_34(x) + F_35(x) + F_39(x))
Eq(F_34(x), 0)
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_12(x))
Eq(F_38(x), F_33(x))
Eq(F_39(x), F_12(x)*F_29(x))
Eq(F_40(x), F_34(x) + F_41(x) + F_64(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_49(x))
Eq(F_43(x), F_44(x) + F_8(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_12(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_12(x))
Eq(F_48(x), F_44(x))
Eq(F_49(x), F_40(x) + F_50(x))
Eq(F_50(x), 2*F_34(x) + F_51(x) + F_55(x))
Eq(F_51(x), F_12(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), F_44(x))
Eq(F_54(x), F_50(x))
Eq(F_55(x), F_12(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_63(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_1(x) + F_60(x))
Eq(F_63(x), F_55(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_60(x) + F_67(x))
Eq(F_67(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_77(x))
Eq(F_71(x), F_34(x) + F_64(x) + F_72(x))
Eq(F_72(x), F_12(x)*F_73(x))
Eq(F_73(x), F_60(x) + F_74(x))
Eq(F_74(x), F_34(x) + F_72(x) + F_75(x))
Eq(F_75(x), F_12(x)*F_76(x))
Eq(F_76(x), F_60(x) + F_74(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_12(x)*F_79(x))
Eq(F_79(x), F_58(x) + F_80(x))
Eq(F_80(x), F_78(x))
Eq(F_81(x), F_33(x) + F_82(x))
Eq(F_82(x), 2*F_34(x) + F_83(x) + F_87(x))
Eq(F_83(x), F_12(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_18(x))
Eq(F_86(x), F_82(x))
Eq(F_87(x), F_12(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_90(x))
Eq(F_89(x), F_58(x))
Eq(F_90(x), F_87(x))
Eq(F_91(x), F_12(x)*F_92(x))
Eq(F_92(x), F_1(x) + F_118(x) + F_180(x) + F_93(x))
Eq(F_93(x), F_94(x, 1))
Eq(F_94(x, k_0), F_13(x, k_0)*F_95(x, k_0))
Eq(F_95(x, k_0), F_1(x) + F_94(x, k_0) + F_96(x, k_0) + F_98(x, k_0))
Eq(F_96(x, k_0), F_12(x)*F_97(x, k_0))
Eq(F_97(x, k_0), (-k_0*F_95(x, k_0) + F_95(x, 1))/(1 - k_0))
Eq(F_98(x, k_0), F_12(x)*F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x) + F_101(x, k_0))
Eq(F_100(x), F_62(x) + F_76(x))
Eq(F_101(x, k_0), F_102(x, k_0) + F_110(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0) + F_106(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0)*F_13(x, k_0))
Eq(F_105(x, k_0), F_1(x) + F_103(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0) + F_109(x, k_0) + F_34(x))
Eq(F_107(x, k_0), F_108(x, k_0)*F_13(x, k_0))
Eq(F_108(x, k_0), F_106(x, k_0) + F_60(x))
Eq(F_109(x, k_0), F_102(x, k_0)*F_12(x))
Eq(F_110(x, k_0), F_111(x, k_0) + F_114(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0)*F_12(x))
Eq(F_113(x, k_0), F_103(x, k_0) + F_111(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0) + F_117(x, k_0) + 2*F_34(x))
Eq(F_115(x, k_0), F_116(x, k_0)*F_12(x))
Eq(F_116(x, k_0), F_106(x, k_0) + F_114(x, k_0))
Eq(F_117(x, k_0), F_110(x, k_0)*F_12(x))
Eq(F_118(x), F_119(x)*F_12(x))
Eq(F_119(x), F_120(x, 1))
Eq(F_120(x, k_0), F_1(x) + F_121(x, k_0) + F_123(x, k_0) + F_125(x, k_0) + F_94(x, k_0))
Eq(F_121(x, k_0), F_12(x)*F_122(x, k_0))
Eq(F_122(x, k_0), (k_0*F_95(x, k_0) - F_95(x, 1))/(k_0 - 1))
Eq(F_123(x, k_0), F_12(x)*F_124(x, k_0))
Eq(F_124(x, k_0), (-k_0*F_120(x, k_0) + F_120(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, k_0) + F_99(x, k_0))
Eq(F_127(x, k_0), F_128(x) + F_156(x, k_0))
Eq(F_128(x), F_129(x) + F_76(x))
Eq(F_129(x), F_130(x) + F_136(x))
Eq(F_130(x), F_131(x) + F_134(x) + F_34(x))
Eq(F_131(x), F_12(x)*F_132(x))
Eq(F_132(x), F_12(x) + F_133(x))
Eq(F_133(x), F_131(x) + F_34(x) + F_59(x))
Eq(F_134(x), F_12(x)*F_135(x))
Eq(F_135(x), F_130(x) + F_60(x))
Eq(F_136(x), F_137(x) + F_146(x) + F_148(x) + F_34(x))
Eq(F_137(x), F_12(x)*F_138(x))
Eq(F_138(x), F_139(x) + F_142(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_12(x)*F_141(x))
Eq(F_141(x), F_12(x) + F_139(x))
Eq(F_142(x), F_137(x) + F_143(x) + 2*F_34(x))
Eq(F_143(x), F_12(x)*F_144(x))
Eq(F_144(x), F_145(x) + F_58(x))
Eq(F_145(x), F_143(x))
Eq(F_146(x), F_12(x)*F_147(x))
Eq(F_147(x), F_136(x) + F_74(x))
Eq(F_148(x), F_12(x)*F_149(x))
Eq(F_149(x), F_150(x) + F_153(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_12(x)*F_152(x))
Eq(F_152(x), F_150(x) + F_60(x))
Eq(F_153(x), F_148(x) + F_154(x) + 2*F_34(x))
Eq(F_154(x), F_12(x)*F_155(x))
Eq(F_155(x), F_153(x) + F_74(x))
Eq(F_156(x, k_0), F_157(x, k_0) + F_165(x, k_0))
Eq(F_157(x, k_0), F_158(x, k_0) + F_161(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0))
Eq(F_159(x, k_0), F_13(x, k_0)*F_160(x, k_0))
Eq(F_160(x, k_0), F_158(x, k_0) + F_60(x))
Eq(F_161(x, k_0), F_162(x, k_0) + F_164(x, k_0) + 2*F_34(x))
Eq(F_162(x, k_0), F_13(x, k_0)*F_163(x, k_0))
Eq(F_163(x, k_0), F_161(x, k_0) + F_74(x))
Eq(F_164(x, k_0), F_12(x)*F_157(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0) + F_169(x, k_0))
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_158(x, k_0) + F_166(x, k_0))
Eq(F_169(x, k_0), F_170(x, k_0) + F_172(x, k_0) + 3*F_34(x))
Eq(F_170(x, k_0), F_12(x)*F_171(x, k_0))
Eq(F_171(x, k_0), F_161(x, k_0) + F_169(x, k_0))
Eq(F_172(x, k_0), F_12(x)*F_173(x, k_0))
Eq(F_173(x, k_0), F_174(x, k_0) + F_177(x, k_0))
Eq(F_174(x, k_0), F_175(x, k_0))
Eq(F_175(x, k_0), F_12(x)*F_176(x, k_0))
Eq(F_176(x, k_0), F_158(x, k_0) + F_174(x, k_0))
Eq(F_177(x, k_0), F_172(x, k_0) + F_178(x, k_0) + 3*F_34(x))
Eq(F_178(x, k_0), F_12(x)*F_179(x, k_0))
Eq(F_179(x, k_0), F_161(x, k_0) + F_177(x, k_0))
Eq(F_180(x), F_12(x)*F_181(x))
Eq(F_181(x), F_100(x) + F_128(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 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], [0, 0]]}, {"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], [2, 0], [2, 0], [2, 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, 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": [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"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"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], [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], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 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, 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": [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], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"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], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": 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