0132_1203_3012
Counting sequence:
1, 1, 2, 6, 21, 74, 254, 858, 2889, 9775, 33371, 115135, 401538, 1414821, 5032193, 18049762, 65227297, 237274644, 868165894, 3192968853, 11797236312, 43767229452, 162975158274, 608896489079, 2281826837352, 8574803667788, 32304855823168, 121990404283599, 461657855566614, 1750582925032422, 6650460281519824, 25308845356681838, 96470637002285349, 368277775208101071, 1407903769293799727, 5389528096873925067, 20657380968938971738, 79271272060268921185, 304539958243497052097, 1171209887382235155027, 4508824093497287229972, 17374323893646324019343, 67011320004289378576649, 258681354400924416321057, 999404189426442817156300, 3864202673112250322012523, 14952232025760984491660815, 57898228199047924367714543, 224349067244000698652885740, 869902315598015770219397753, 3375142992745305112780957563, 13103227935128527611681528197, 50900078658320334653117809236, 197834879654885166103351034401, 769347052860213514409642814285, 2993422594143959271414058989505, 11652841492402809187731017742230, 45384329084266833633048483248377, 176840971161219789360101266216739, 689375355760336407629315450681289, 2688548434085847778774293734705252, 10489696279617361238015089974014421, 40943494095430346071820484591175357, 159874103712488304229304158529880306, 624506753838108507827166761011928497, 2440376152875485725352402883622911068, 9539642089025943629035094447964947878, 37304253141253797045391028393367350693, 145925460902631923250980559194049182544, 571012937632917208272342508641677498492, 2235109762822886839801248588145484390058, 8751567648187898928154132799987040540283, 34277028826207200679958896166496935547948, 134291085740588246737965667461273596980864, 526277050423069636065970903798838378139692, 2063011185481866009681465571906252141150663, 8089197571001455905530046419394465645468758, 31726556953797993262943896926705206421465498, 124466115974798818704578182686518864110441124, 488412969561535633103879518503386878287494607, 1917027609974440475623787429833533337951324428, 7526135827078548857146604901851298447458557618, 29553962103912343438724953170065035530632843438, 116079869927498432473438120638751188802756712359, 456029887329841752683741675676393063888097791282, 1791936556181289236346145588093461529354963536408, 7042756897684642214389049547436995949966489826618, 27685438320068391099696374740520155135855007380993, 108854581517557709533465090600357892913865631784694, 428081695845871987084482188168173610018074896034702, 1683795490172550510941429498730293197687347630550098, 6624192232210463978892720052628669632613568302033423, 26064874491574796914298801619762569182865670365177038, 102578361362630207218443351687522129740750890788471664, 403767744684168906969327720972808285253274499016086742, 1589577194286511795566642010227429524516757951663324603, 6258989204030698666414812569503155307428137239860730408, 24648917405058426619604553430995673851835140441132432328, 97087004446302015177940781351221311938335518149228818704, 382465740896934905884027426908755794164666964539402752707, 1506922052959310942517445979210742709944227018976487929438
Generating function in Maple syntax:
1/2*((-2*x^6+x^5+7*x^4-13*x^3+11*x^2-5*x+1)*(1-4*x)^(1/2)+6*x^6-3*x^5-5*x^4+9*x^3-9*x^2+5*x-1)/x/(2*x-1)/(x-1)^4
Generating function in latex syntax:
\frac{\left(-2 x^{6}+x^{5}+7 x^{4}-13 x^{3}+11 x^{2}-5 x +1\right) \sqrt{1-4 x}+6 x^{6}-3 x^{5}-5 x^{4}+9 x^{3}-9 x^{2}+5 x -1}{2 x \left(2 x -1\right) \left(x -1\right)^{4}}
Generating function in sympy syntax:
(3*x**6 - 3*x**5/2 - 5*x**4/2 + 9*x**3/2 - 9*x**2/2 + 5*x/2 + sqrt(1 - 4*x)*(-2*x**6 + x**5 + 7*x**4 - 13*x**3 + 11*x**2 - 5*x + 1)/2 - 1/2)/(x*(x - 1)**4*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*(x-1)^8*F(x)^2-(2*x-1)*(6*x^6-3*x^5-5*x^4+9*x^3-9*x^2+5*x-1)*(x-1)^4*F(x)+4*x^12+4*x^11-35*x^10+60*x^9-3*x^8-169*x^7+350*x^6-399*x^5+302*x^4-157*x^3+54*x^2-11*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} \left(x -1\right)^{8} F \! \left(x \right)^{2}-\left(2 x -1\right) \left(6 x^{6}-3 x^{5}-5 x^{4}+9 x^{3}-9 x^{2}+5 x -1\right) \left(x -1\right)^{4} F \! \left(x \right)+4 x^{12}+4 x^{11}-35 x^{10}+60 x^{9}-3 x^{8}-169 x^{7}+350 x^{6}-399 x^{5}+302 x^{4}-157 x^{3}+54 x^{2}-11 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 74
a(6) = 254
a(7) = 858
a(8) = 2889
a(9) = 9775
a(10) = 33371
a(11) = 115135
a(12) = 401538
a(n+8) = 8*(2*n-1)/(n+9)*a(n)-4*(5*n-13)/(n+9)*a(n+1)-6*(8*n+33)/(n+9)*a(n+2)+(529+145*n)/(n+9)*a(n+3)-(173*n+791)/(n+9)*a(n+4)+7*(17*n+97)/(n+9)*a(n+5)-(49*n+335)/(n+9)*a(n+6)+(87+11*n)/(n+9)*a(n+7)+1/2*(n^3-12*n^2+47*n-48)/(n+9), n >= 13
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 21
a \! \left(5\right) = 74
a \! \left(6\right) = 254
a \! \left(7\right) = 858
a \! \left(8\right) = 2889
a \! \left(9\right) = 9775
a \! \left(10\right) = 33371
a \! \left(11\right) = 115135
a \! \left(12\right) = 401538
a \! \left(n +8\right) = \frac{8 \left(2 n -1\right) a \! \left(n \right)}{n +9}-\frac{4 \left(5 n -13\right) a \! \left(n +1\right)}{n +9}-\frac{6 \left(8 n +33\right) a \! \left(n +2\right)}{n +9}+\frac{\left(529+145 n \right) a \! \left(n +3\right)}{n +9}-\frac{\left(173 n +791\right) a \! \left(n +4\right)}{n +9}+\frac{7 \left(17 n +97\right) a \! \left(n +5\right)}{n +9}-\frac{\left(49 n +335\right) a \! \left(n +6\right)}{n +9}+\frac{\left(87+11 n \right) a \! \left(n +7\right)}{n +9}+\frac{n^{3}-12 n^{2}+47 n -48}{2 n +18}, \quad n \geq 13
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/291/
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[106,x]+F[4,x]
F[4,x] = F[12,x]*F[5,x]
F[5,x] = F[53,x]+F[6,x]
F[6,x] = F[21,x]+F[7,x]
F[7,x] = F[1,x]+F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[12,x]
F[10,x] = F[11,x]+F[13,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = x
F[13,x] = F[14,x]+F[8,x]
F[14,x] = F[15,x]+F[16,x]+F[20,x]
F[15,x] = 0
F[16,x] = F[12,x]*F[17,x]
F[17,x] = F[18,x]+F[19,x]
F[18,x] = F[12,x]
F[19,x] = F[14,x]
F[20,x] = F[12,x]*F[8,x]
F[21,x] = F[22,x]+F[40,x]
F[22,x] = F[23,x]
F[23,x] = F[12,x]*F[24,x]
F[24,x] = F[25,x]+F[28,x]
F[25,x] = F[1,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[12,x]*F[25,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[30,x]
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[1,x]+F[29,x]
F[32,x] = F[15,x]+F[33,x]+F[35,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[26,x]+F[32,x]
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[29,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[12,x]*F[39,x]
F[39,x] = F[26,x]+F[37,x]
F[40,x] = F[41,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[43,x]+F[46,x]
F[43,x] = F[22,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[12,x]*F[22,x]
F[46,x] = F[40,x]+F[47,x]
F[47,x] = 2*F[15,x]+F[48,x]+F[52,x]
F[48,x] = F[12,x]*F[49,x]
F[49,x] = F[50,x]+F[51,x]
F[50,x] = F[44,x]
F[51,x] = F[47,x]
F[52,x] = F[12,x]*F[40,x]
F[53,x] = F[54,x]+F[74,x]
F[54,x] = F[29,x]+F[55,x]
F[55,x] = F[15,x]+F[56,x]+F[58,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[55,x]+F[8,x]
F[58,x] = F[12,x]*F[59,x]
F[59,x] = F[60,x]+F[64,x]
F[60,x] = F[29,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[12,x]*F[63,x]
F[63,x] = F[12,x]+F[61,x]
F[64,x] = F[55,x]+F[65,x]
F[65,x] = 2*F[15,x]+F[66,x]+F[70,x]
F[66,x] = F[12,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[20,x]
F[69,x] = F[66,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[61,x]
F[73,x] = F[65,x]
F[74,x] = F[75,x]+F[87,x]
F[75,x] = F[15,x]+F[76,x]+F[78,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[22,x]+F[75,x]
F[78,x] = F[12,x]*F[79,x]
F[79,x] = F[36,x]+F[80,x]
F[80,x] = F[81,x]+F[84,x]
F[81,x] = F[82,x]
F[82,x] = F[12,x]*F[83,x]
F[83,x] = F[29,x]+F[81,x]
F[84,x] = F[85,x]
F[85,x] = F[12,x]*F[86,x]
F[86,x] = F[37,x]+F[84,x]
F[87,x] = 2*F[15,x]+F[88,x]+F[90,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[40,x]+F[87,x]
F[90,x] = F[12,x]*F[91,x]
F[91,x] = F[92,x]+F[96,x]
F[92,x] = F[75,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[12,x]*F[95,x]
F[95,x] = F[44,x]+F[93,x]
F[96,x] = F[87,x]+F[97,x]
F[97,x] = 3*F[15,x]+F[102,x]+F[98,x]
F[98,x] = F[12,x]*F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[52,x]
F[101,x] = F[98,x]
F[102,x] = F[103,x]*F[12,x]
F[103,x] = F[104,x]+F[105,x]
F[104,x] = F[93,x]
F[105,x] = F[97,x]
F[106,x] = F[107,x]*F[12,x]
F[107,x] = F[108,x,1]
F[108,x,k[0]] = F[1,x]+F[109,x,k[0]]+F[150,x,k[0]]+F[152,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]*F[12,x]
F[110,x,k[0]] = F[111,x,k[0]]+F[127,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[120,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]+F[117,x,k[0]]
F[113,x,k[0]] = F[1,x]+F[114,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]
F[115,x,k[0]] = F[113,x,k[0]]*F[116,x,k[0]]
F[116,x,k[0]] = k[0]*x
F[117,x,k[0]] = F[118,x,k[0]]+F[8,x]
F[118,x,k[0]] = F[119,x,k[0]]
F[119,x,k[0]] = F[116,x,k[0]]*F[117,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]+F[124,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]+F[22,x]
F[122,x,k[0]] = F[123,x,k[0]]
F[123,x,k[0]] = F[116,x,k[0]]*F[121,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]+F[40,x]
F[125,x,k[0]] = F[126,x,k[0]]
F[126,x,k[0]] = F[116,x,k[0]]*F[124,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]+F[139,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]+F[134,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]+F[29,x]
F[130,x,k[0]] = F[131,x,k[0]]+F[133,x,k[0]]+F[15,x]
F[131,x,k[0]] = F[12,x]*F[132,x,k[0]]
F[132,x,k[0]] = F[114,x,k[0]]+F[130,x,k[0]]
F[133,x,k[0]] = F[116,x,k[0]]*F[129,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]+F[55,x]
F[135,x,k[0]] = 2*F[15,x]+F[136,x,k[0]]+F[138,x,k[0]]
F[136,x,k[0]] = F[12,x]*F[137,x,k[0]]
F[137,x,k[0]] = F[118,x,k[0]]+F[135,x,k[0]]
F[138,x,k[0]] = F[116,x,k[0]]*F[134,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]+F[145,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]+F[75,x]
F[141,x,k[0]] = 2*F[15,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[122,x,k[0]]+F[141,x,k[0]]
F[144,x,k[0]] = F[116,x,k[0]]*F[140,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]+F[87,x]
F[146,x,k[0]] = 3*F[15,x]+F[147,x,k[0]]+F[149,x,k[0]]
F[147,x,k[0]] = F[12,x]*F[148,x,k[0]]
F[148,x,k[0]] = F[125,x,k[0]]+F[146,x,k[0]]
F[149,x,k[0]] = F[116,x,k[0]]*F[145,x,k[0]]
F[150,x,k[0]] = F[12,x]*F[151,x,k[0]]
F[151,x,k[0]] = 1/(-1+k[0])*(F[108,x,k[0]]*k[0]-F[108,x,1])
F[152,x,k[0]] = F[108,x,k[0]]*F[116,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{12}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{106}\! \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_{53}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{21}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{13}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{8}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{20}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right)
F_{19}\! \left(x \right) = F_{14}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{40}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \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_{1}\! \left(x \right)+F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{15}\! \left(x \right)+F_{33}\! \left(x \right)+F_{35}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{26}\! \left(x \right)+F_{32}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{29}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{26}\! \left(x \right)+F_{37}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{43}\! \left(x \right) = F_{22}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{46}\! \left(x \right) = F_{40}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{48}\! \left(x \right)+F_{52}\! \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_{44}\! \left(x \right)
F_{51}\! \left(x \right) = F_{47}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{74}\! \left(x \right)
F_{54}\! \left(x \right) = F_{29}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{15}\! \left(x \right)+F_{56}\! \left(x \right)+F_{58}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{55}\! \left(x \right)+F_{8}\! \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_{64}\! \left(x \right)
F_{60}\! \left(x \right) = F_{29}\! \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_{12}\! \left(x \right)+F_{61}\! \left(x \right)
F_{64}\! \left(x \right) = F_{55}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{66}\! \left(x \right)+F_{70}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{20}\! \left(x \right)
F_{69}\! \left(x \right) = F_{66}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{61}\! \left(x \right)
F_{73}\! \left(x \right) = F_{65}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{87}\! \left(x \right)
F_{75}\! \left(x \right) = F_{15}\! \left(x \right)+F_{76}\! \left(x \right)+F_{78}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{22}\! \left(x \right)+F_{75}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{36}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{84}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{29}\! \left(x \right)+F_{81}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{12}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{37}\! \left(x \right)+F_{84}\! \left(x \right)
F_{87}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{88}\! \left(x \right)+F_{90}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{40}\! \left(x \right)+F_{87}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{96}\! \left(x \right)
F_{92}\! \left(x \right) = F_{75}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{44}\! \left(x \right)+F_{93}\! \left(x \right)
F_{96}\! \left(x \right) = F_{87}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{102}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{52}\! \left(x \right)
F_{101}\! \left(x \right) = F_{98}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{12}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{105}\! \left(x \right)
F_{104}\! \left(x \right) = F_{93}\! \left(x \right)
F_{105}\! \left(x \right) = F_{97}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{12}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x , 1\right)
F_{108}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{109}\! \left(x , y\right)+F_{150}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{120}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{117}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{116}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = y x
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{117}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{124}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{22}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{121}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{40}\! \left(x \right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{124}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{139}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{133}\! \left(x , y\right)+F_{15}\! \left(x \right)
F_{131}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{132}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{130}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{129}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{55}\! \left(x \right)
F_{135}\! \left(x , y\right) = 2 F_{15}\! \left(x \right)+F_{136}\! \left(x , y\right)+F_{138}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{137}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{135}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{134}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{145}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{75}\! \left(x \right)
F_{141}\! \left(x , y\right) = 2 F_{15}\! \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_{122}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{140}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)+F_{87}\! \left(x \right)
F_{146}\! \left(x , y\right) = 3 F_{15}\! \left(x \right)+F_{147}\! \left(x , y\right)+F_{149}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{148}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{146}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{145}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{151}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = \frac{F_{108}\! \left(x , y\right) y -F_{108}\! \left(x , 1\right)}{-1+y}
F_{152}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{116}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_12(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_106(x) + F_4(x))
Eq(F_4(x), F_12(x)*F_5(x))
Eq(F_5(x), F_53(x) + F_6(x))
Eq(F_6(x), F_21(x) + F_7(x))
Eq(F_7(x), F_1(x) + F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_12(x))
Eq(F_10(x), F_11(x) + F_13(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_8(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_20(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_12(x)*F_17(x))
Eq(F_17(x), F_18(x) + F_19(x))
Eq(F_18(x), F_12(x))
Eq(F_19(x), F_14(x))
Eq(F_20(x), F_12(x)*F_8(x))
Eq(F_21(x), F_22(x) + F_40(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_12(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_28(x))
Eq(F_25(x), F_1(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_12(x)*F_25(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_1(x) + F_29(x))
Eq(F_32(x), F_15(x) + F_33(x) + F_35(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_26(x) + F_32(x))
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_29(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_12(x)*F_39(x))
Eq(F_39(x), F_26(x) + F_37(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_46(x))
Eq(F_43(x), F_22(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_12(x)*F_22(x))
Eq(F_46(x), F_40(x) + F_47(x))
Eq(F_47(x), 2*F_15(x) + F_48(x) + F_52(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_44(x))
Eq(F_51(x), F_47(x))
Eq(F_52(x), F_12(x)*F_40(x))
Eq(F_53(x), F_54(x) + F_74(x))
Eq(F_54(x), F_29(x) + F_55(x))
Eq(F_55(x), F_15(x) + F_56(x) + F_58(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_55(x) + F_8(x))
Eq(F_58(x), F_12(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_64(x))
Eq(F_60(x), F_29(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_12(x) + F_61(x))
Eq(F_64(x), F_55(x) + F_65(x))
Eq(F_65(x), 2*F_15(x) + F_66(x) + F_70(x))
Eq(F_66(x), F_12(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_20(x))
Eq(F_69(x), F_66(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_61(x))
Eq(F_73(x), F_65(x))
Eq(F_74(x), F_75(x) + F_87(x))
Eq(F_75(x), F_15(x) + F_76(x) + F_78(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_22(x) + F_75(x))
Eq(F_78(x), F_12(x)*F_79(x))
Eq(F_79(x), F_36(x) + F_80(x))
Eq(F_80(x), F_81(x) + F_84(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_12(x)*F_83(x))
Eq(F_83(x), F_29(x) + F_81(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_12(x)*F_86(x))
Eq(F_86(x), F_37(x) + F_84(x))
Eq(F_87(x), 2*F_15(x) + F_88(x) + F_90(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_40(x) + F_87(x))
Eq(F_90(x), F_12(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_96(x))
Eq(F_92(x), F_75(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_12(x)*F_95(x))
Eq(F_95(x), F_44(x) + F_93(x))
Eq(F_96(x), F_87(x) + F_97(x))
Eq(F_97(x), F_102(x) + 3*F_15(x) + F_98(x))
Eq(F_98(x), F_12(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_52(x))
Eq(F_101(x), F_98(x))
Eq(F_102(x), F_103(x)*F_12(x))
Eq(F_103(x), F_104(x) + F_105(x))
Eq(F_104(x), F_93(x))
Eq(F_105(x), F_97(x))
Eq(F_106(x), F_107(x)*F_12(x))
Eq(F_107(x), F_108(x, 1))
Eq(F_108(x, k_0), F_1(x) + F_109(x, k_0) + F_150(x, k_0) + F_152(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0)*F_12(x))
Eq(F_110(x, k_0), F_111(x, k_0) + F_127(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_120(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0) + F_117(x, k_0))
Eq(F_113(x, k_0), F_1(x) + F_114(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0))
Eq(F_115(x, k_0), F_113(x, k_0)*F_116(x, k_0))
Eq(F_116(x, k_0), k_0*x)
Eq(F_117(x, k_0), F_118(x, k_0) + F_8(x))
Eq(F_118(x, k_0), F_119(x, k_0))
Eq(F_119(x, k_0), F_116(x, k_0)*F_117(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0) + F_124(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0) + F_22(x))
Eq(F_122(x, k_0), F_123(x, k_0))
Eq(F_123(x, k_0), F_116(x, k_0)*F_121(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0) + F_40(x))
Eq(F_125(x, k_0), F_126(x, k_0))
Eq(F_126(x, k_0), F_116(x, k_0)*F_124(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0) + F_139(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0) + F_134(x, k_0))
Eq(F_129(x, k_0), F_130(x, k_0) + F_29(x))
Eq(F_130(x, k_0), F_131(x, k_0) + F_133(x, k_0) + F_15(x))
Eq(F_131(x, k_0), F_12(x)*F_132(x, k_0))
Eq(F_132(x, k_0), F_114(x, k_0) + F_130(x, k_0))
Eq(F_133(x, k_0), F_116(x, k_0)*F_129(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0) + F_55(x))
Eq(F_135(x, k_0), F_136(x, k_0) + F_138(x, k_0) + 2*F_15(x))
Eq(F_136(x, k_0), F_12(x)*F_137(x, k_0))
Eq(F_137(x, k_0), F_118(x, k_0) + F_135(x, k_0))
Eq(F_138(x, k_0), F_116(x, k_0)*F_134(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0) + F_145(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0) + F_75(x))
Eq(F_141(x, k_0), F_142(x, k_0) + F_144(x, k_0) + 2*F_15(x))
Eq(F_142(x, k_0), F_12(x)*F_143(x, k_0))
Eq(F_143(x, k_0), F_122(x, k_0) + F_141(x, k_0))
Eq(F_144(x, k_0), F_116(x, k_0)*F_140(x, k_0))
Eq(F_145(x, k_0), F_146(x, k_0) + F_87(x))
Eq(F_146(x, k_0), F_147(x, k_0) + F_149(x, k_0) + 3*F_15(x))
Eq(F_147(x, k_0), F_12(x)*F_148(x, k_0))
Eq(F_148(x, k_0), F_125(x, k_0) + F_146(x, k_0))
Eq(F_149(x, k_0), F_116(x, k_0)*F_145(x, k_0))
Eq(F_150(x, k_0), F_12(x)*F_151(x, k_0))
Eq(F_151(x, k_0), (k_0*F_108(x, k_0) - F_108(x, 1))/(k_0 - 1))
Eq(F_152(x, k_0), F_108(x, k_0)*F_116(x, k_0))
Pack JSON:
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Specification JSON:
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