0132_0213_0231_1023_1230
Counting sequence:
1, 1, 2, 6, 19, 60, 192, 625, 2073, 6999, 24009, 83502, 293865, 1044685, 3746192, 13534810, 49221332, 180031647, 661839164, 2444131541, 9062807635, 33728304306, 125942291971, 471699822487, 1771597431122, 6670701477771, 25176688220071, 95229090065070, 360924430561897, 1370494833290179, 5213124263278016, 19862264967393376, 75792225388975918, 289630998227293191, 1108288564849724766, 4246334862695027911, 16289141640843232295, 62557051291102970544, 240503971838185149485, 925575792148781724563, 3565522139151830539104, 13747857288421527895897, 53055256925471334485031, 204920547785063823798788, 792117575799989509278599, 3064258068545311610711167, 11862550757080392465287346, 45955164609146506196086243, 178148167042785842676065449, 691046474362825266650284454, 2682259627162411350585702969, 10417211628617766498934203107, 40480824298617026007983940560, 157392860054746749718617398935, 612279449765030304838837615251, 2383059888027040865349238626766, 9279678676153208762039571351025, 36152317086318329189193941505059, 140908584507140149616189693327880, 549452486936415739134232198823075, 2143422622893778775499451131465107, 8364969612998350875356622415325326, 32658334019214059448150115870657737, 127553175267803414418268269606107956, 498368813461203650869228888796822995, 1947904973578109127546340209154142864, 7616180351165036874142540376140183884, 29788912603672927136695934262393864398, 116550916796087017333157709702142146332, 456158925303459089828284969099688540380, 1785879301498911574461840662714302172862, 6993903724939299962426096391690296696392, 27397765805217113153770209652013951725654, 107358166862167403127495661304868222045596, 420800350664132331996454223713441601056440, 1649813792201891769248573370825668043982856, 6470062705553147313594669273782815703152076, 25380126691823441525088306910169257675566712, 99583628424115364575215981108196576026238848, 390830284634030517068048386560374191311923230, 1534235104667139810539995731539503349573190378, 6024160114502693452157311417721872627881040518, 23659170575664008926046530944142873389918459006, 92939122195011240331697020222022592520617436944, 365166868744465269969187632639912243511311287370, 1435078667713353374731298118352826991975650688454, 5640913717842168066478651063839809480352056803604, 22177396066259279284277415021622877590551523202038, 87208136593385563150764971085394484616433260547802, 342994296055423687427411986096925215691735814067180, 1349268458028735691340010425271952497064581038909842, 5308717568778400353290825905867239393981119625713222, 20890985090194669873305810603602151611610623330481264, 82225132359929126510711947266999148523424979093657886, 323686792912124907460387353957536330399528467104509350, 1274437488891649936665114281134867083636200544397797686, 5018613264156311808768993836267343701846985152485333736, 19766012965682031969429464316980827227352629062059752872, 77861567297056318966969682349456841006673608383688099258, 306757038496432170775637938674090242768645458399010450070, 1208737265457889053210573112642947827100422901745788092548
Generating function in Maple syntax:
1/2*(-(1-4*x)^(1/2)*x^3-(1-4*x)^(1/2)*x^2+3*x^3+3*x^2+(1-4*x)^(1/2)-1)/(x^2+x-1)/x
Generating function in latex syntax:
\frac{-\sqrt{1-4 x}\, x^{3}-\sqrt{1-4 x}\, x^{2}+3 x^{3}+3 x^{2}+\sqrt{1-4 x}-1}{2 \left(x^{2}+x -1\right) x}
Generating function in sympy syntax:
(-x**3*sqrt(1 - 4*x)/2 + 3*x**3/2 - x**2*sqrt(1 - 4*x)/2 + 3*x**2/2 + sqrt(1 - 4*x)/2 - 1/2)/(x*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
x*(x^2+x-1)^2*F(x)^2-(x^2+x-1)*(3*x^3+3*x^2-1)*F(x)+x^6+4*x^5+5*x^4-3*x^2-x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(x^{2}+x -1\right)^{2} F \! \left(x \right)^{2}-\left(x^{2}+x -1\right) \left(3 x^{3}+3 x^{2}-1\right) F \! \left(x \right)+x^{6}+4 x^{5}+5 x^{4}-3 x^{2}-x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 60
a(6) = 192
a(n+6) = 2*(-1+2*n)/(n+7)*a(n)+(3+7*n)/(n+7)*a(1+n)-2*(n-2)/(n+7)*a(n+2)-2*(15+4*n)/(n+7)*a(n+3)-2*(n+6)/(n+7)*a(n+4)+(29+5*n)/(n+7)*a(n+5), n >= 7
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) = 60
a \! \left(6\right) = 192
a \! \left(n +6\right) = \frac{2 \left(-1+2 n \right) a \! \left(n \right)}{n +7}+\frac{\left(3+7 n \right) a \! \left(1+n \right)}{n +7}-\frac{2 \left(n -2\right) a \! \left(n +2\right)}{n +7}-\frac{2 \left(15+4 n \right) a \! \left(n +3\right)}{n +7}-\frac{2 \left(n +6\right) a \! \left(n +4\right)}{n +7}+\frac{\left(29+5 n \right) a \! \left(n +5\right)}{n +7}, \quad n \geq 7
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21557/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[15,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[61,x]
F[4,x] = F[5,x]
F[5,x] = F[15,x]*F[6,x]
F[6,x] = F[59,x]+F[7,x]
F[7,x] = F[22,x]+F[8,x]
F[8,x] = F[1,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[15,x]
F[11,x] = F[12,x]+F[16,x]
F[12,x] = F[1,x]+F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[12,x]*F[15,x]
F[15,x] = x
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[18,x]
F[18,x] = F[15,x]*F[19,x]
F[19,x] = F[1,x]+F[17,x]
F[20,x] = F[21,x]
F[21,x] = F[15,x]*F[16,x]
F[22,x] = F[23,x]+F[30,x]
F[23,x] = F[24,x]
F[24,x] = F[15,x]*F[25,x]
F[25,x] = F[26,x]+F[27,x]
F[26,x] = F[1,x]+F[15,x]
F[27,x] = F[23,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[15,x]*F[23,x]
F[30,x] = F[31,x]+F[32,x]+F[42,x]
F[31,x] = 0
F[32,x] = F[15,x]*F[33,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = F[17,x]
F[35,x] = F[36,x]
F[36,x] = F[31,x]+F[32,x]+F[37,x]
F[37,x] = F[15,x]*F[38,x]
F[38,x] = F[17,x]+F[39,x]
F[39,x] = F[31,x]+F[37,x]+F[40,x]
F[40,x] = F[15,x]*F[41,x]
F[41,x] = F[17,x]+F[39,x]
F[42,x] = F[15,x]*F[43,x]
F[43,x] = F[44,x]+F[51,x]
F[44,x] = F[17,x]+F[45,x]
F[45,x] = F[31,x]+F[46,x]+F[50,x]
F[46,x] = F[15,x]*F[47,x]
F[47,x] = F[15,x]+F[48,x]
F[48,x] = F[31,x]+F[46,x]+F[49,x]
F[49,x] = F[15,x]*F[17,x]
F[50,x] = F[15,x]*F[44,x]
F[51,x] = F[39,x]+F[52,x]
F[52,x] = 2*F[31,x]+F[53,x]+F[58,x]
F[53,x] = F[15,x]*F[54,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[49,x]
F[56,x] = 2*F[31,x]+F[53,x]+F[57,x]
F[57,x] = F[15,x]*F[39,x]
F[58,x] = F[15,x]*F[51,x]
F[59,x] = F[12,x]*F[15,x]*F[60,x]
F[60,x] = F[1,x]+F[23,x]
F[61,x] = F[15,x]*F[62,x]
F[62,x] = F[63,x,1]
F[63,x,k[0]] = F[1,x]+F[64,x,k[0]]+F[66,x,k[0]]+F[68,x,k[0]]
F[64,x,k[0]] = F[63,x,k[0]]*F[65,x,k[0]]
F[65,x,k[0]] = k[0]*x
F[66,x,k[0]] = F[15,x]*F[67,x,k[0]]
F[67,x,k[0]] = (F[63,x,k[0]]*k[0]-F[63,x,1])/(-1+k[0])
F[68,x,k[0]] = F[69,x,k[0]]
F[69,x,k[0]] = F[15,x]*F[70,x,k[0]]
F[70,x,k[0]] = F[141,x,k[0]]+F[71,x,k[0]]
F[71,x,k[0]] = F[7,x]+F[72,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]+F[99,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]+F[77,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]
F[75,x,k[0]] = F[65,x,k[0]]*F[76,x,k[0]]
F[76,x,k[0]] = F[1,x]+F[74,x,k[0]]
F[77,x,k[0]] = F[31,x]+F[78,x,k[0]]+F[83,x,k[0]]
F[78,x,k[0]] = F[65,x,k[0]]*F[79,x,k[0]]
F[79,x,k[0]] = F[17,x]+F[80,x,k[0]]
F[80,x,k[0]] = F[31,x]+F[78,x,k[0]]+F[81,x,k[0]]
F[81,x,k[0]] = F[15,x]*F[82,x,k[0]]
F[82,x,k[0]] = F[74,x,k[0]]+F[80,x,k[0]]
F[83,x,k[0]] = F[15,x]*F[84,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]+F[92,x,k[0]]
F[85,x,k[0]] = F[74,x,k[0]]+F[86,x,k[0]]
F[86,x,k[0]] = F[31,x]+F[87,x,k[0]]+F[91,x,k[0]]
F[87,x,k[0]] = F[65,x,k[0]]*F[88,x,k[0]]
F[88,x,k[0]] = F[15,x]+F[89,x,k[0]]
F[89,x,k[0]] = F[31,x]+F[87,x,k[0]]+F[90,x,k[0]]
F[90,x,k[0]] = F[15,x]*F[74,x,k[0]]
F[91,x,k[0]] = F[15,x]*F[85,x,k[0]]
F[92,x,k[0]] = F[80,x,k[0]]+F[93,x,k[0]]
F[93,x,k[0]] = 2*F[31,x]+F[94,x,k[0]]+F[98,x,k[0]]
F[94,x,k[0]] = F[65,x,k[0]]*F[95,x,k[0]]
F[95,x,k[0]] = F[55,x]+F[96,x,k[0]]
F[96,x,k[0]] = 2*F[31,x]+F[94,x,k[0]]+F[97,x,k[0]]
F[97,x,k[0]] = F[15,x]*F[80,x,k[0]]
F[98,x,k[0]] = F[15,x]*F[92,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]+F[110,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]+F[104,x,k[0]]+F[31,x]
F[101,x,k[0]] = F[102,x,k[0]]*F[65,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]+F[15,x]
F[103,x,k[0]] = F[90,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]*F[15,x]
F[105,x,k[0]] = F[106,x,k[0]]+F[107,x,k[0]]
F[106,x,k[0]] = F[103,x,k[0]]+F[74,x,k[0]]
F[107,x,k[0]] = F[100,x,k[0]]+F[108,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[100,x,k[0]]*F[15,x]
F[110,x,k[0]] = F[111,x,k[0]]+F[112,x,k[0]]+F[125,x,k[0]]+F[31,x]
F[111,x,k[0]] = 0
F[112,x,k[0]] = F[113,x,k[0]]*F[15,x]
F[113,x,k[0]] = F[114,x,k[0]]+F[115,x,k[0]]
F[114,x,k[0]] = F[80,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]
F[116,x,k[0]] = F[111,x,k[0]]+F[112,x,k[0]]+F[117,x,k[0]]+F[31,x]
F[117,x,k[0]] = F[118,x,k[0]]*F[15,x]
F[118,x,k[0]] = F[119,x,k[0]]+F[122,x,k[0]]
F[119,x,k[0]] = F[120,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]*F[15,x]
F[121,x,k[0]] = F[119,x,k[0]]+F[74,x,k[0]]
F[122,x,k[0]] = 2*F[31,x]+F[117,x,k[0]]+F[123,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]*F[15,x]
F[124,x,k[0]] = F[122,x,k[0]]+F[80,x,k[0]]
F[125,x,k[0]] = F[126,x,k[0]]*F[15,x]
F[126,x,k[0]] = F[127,x,k[0]]+F[134,x,k[0]]
F[127,x,k[0]] = F[119,x,k[0]]+F[128,x,k[0]]
F[128,x,k[0]] = 2*F[31,x]+F[129,x,k[0]]+F[133,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]*F[15,x]
F[130,x,k[0]] = F[131,x,k[0]]+F[89,x,k[0]]
F[131,x,k[0]] = 2*F[31,x]+F[129,x,k[0]]+F[132,x,k[0]]
F[132,x,k[0]] = F[119,x,k[0]]*F[15,x]
F[133,x,k[0]] = F[127,x,k[0]]*F[15,x]
F[134,x,k[0]] = F[122,x,k[0]]+F[135,x,k[0]]
F[135,x,k[0]] = 3*F[31,x]+F[136,x,k[0]]+F[140,x,k[0]]
F[136,x,k[0]] = F[137,x,k[0]]*F[15,x]
F[137,x,k[0]] = F[138,x,k[0]]+F[96,x,k[0]]
F[138,x,k[0]] = 3*F[31,x]+F[136,x,k[0]]+F[139,x,k[0]]
F[139,x,k[0]] = F[122,x,k[0]]*F[15,x]
F[140,x,k[0]] = F[134,x,k[0]]*F[15,x]
F[141,x,k[0]] = F[12,x]*F[142,x,k[0]]*F[15,x]
F[142,x,k[0]] = F[143,x,k[0]]+F[60,x]
F[143,x,k[0]] = F[100,x,k[0]]+F[74,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_{15}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{61}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{15}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{59}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{22}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{1}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{16}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = x
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_{15}\! \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_{15}\! \left(x \right) F_{16}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{30}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{27}\! \left(x \right) = F_{23}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{15}\! \left(x \right) F_{23}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)+F_{42}\! \left(x \right)
F_{31}\! \left(x \right) = 0
F_{32}\! \left(x \right) = F_{15}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{17}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{15}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{17}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{31}\! \left(x \right)+F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{15}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{17}\! \left(x \right)+F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{15}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{51}\! \left(x \right)
F_{44}\! \left(x \right) = F_{17}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{31}\! \left(x \right)+F_{46}\! \left(x \right)+F_{50}\! \left(x \right)
F_{46}\! \left(x \right) = F_{15}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{15}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{31}\! \left(x \right)+F_{46}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{15}\! \left(x \right) F_{17}\! \left(x \right)
F_{50}\! \left(x \right) = F_{15}\! \left(x \right) F_{44}\! \left(x \right)
F_{51}\! \left(x \right) = F_{39}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{53}\! \left(x \right)+F_{58}\! \left(x \right)
F_{53}\! \left(x \right) = F_{15}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{49}\! \left(x \right)
F_{56}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{53}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{15}\! \left(x \right) F_{39}\! \left(x \right)
F_{58}\! \left(x \right) = F_{15}\! \left(x \right) F_{51}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{61}\! \left(x \right) = F_{15}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x , 1\right)
F_{63}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{64}\! \left(x , y\right)+F_{66}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{63}\! \left(x , y\right) F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = y x
F_{66}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = \frac{F_{63}\! \left(x , y\right) y -F_{63}\! \left(x , 1\right)}{-1+y}
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{7}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{65}\! \left(x , y\right) F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{74}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{65}\! \left(x , y\right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{87}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{65}\! \left(x , y\right) F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{87}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{80}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{94}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{65}\! \left(x , y\right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{55}\! \left(x \right)+F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{94}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{110}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{104}\! \left(x , y\right)+F_{31}\! \left(x \right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{65}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{15}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{107}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{108}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{112}\! \left(x , y\right)+F_{125}\! \left(x , y\right)+F_{31}\! \left(x \right)
F_{111}\! \left(x , y\right) = 0
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{112}\! \left(x , y\right)+F_{117}\! \left(x , y\right)+F_{31}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{122}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{121}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{117}\! \left(x , y\right)+F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{124}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{129}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{129}\! \left(x , y\right)+F_{132}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{127}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{134}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{135}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = 3 F_{31}\! \left(x \right)+F_{136}\! \left(x , y\right)+F_{140}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = 3 F_{31}\! \left(x \right)+F_{136}\! \left(x , y\right)+F_{139}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{122}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{134}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{141}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{142}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right)+F_{60}\! \left(x \right)
F_{143}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{74}\! \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_15(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_61(x))
Eq(F_4(x), F_5(x))
Eq(F_5(x), F_15(x)*F_6(x))
Eq(F_6(x), F_59(x) + F_7(x))
Eq(F_7(x), F_22(x) + F_8(x))
Eq(F_8(x), F_1(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_15(x))
Eq(F_11(x), F_12(x) + F_16(x))
Eq(F_12(x), F_1(x) + F_13(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_12(x)*F_15(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_15(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_15(x)*F_16(x))
Eq(F_22(x), F_23(x) + F_30(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_15(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_27(x))
Eq(F_26(x), F_1(x) + F_15(x))
Eq(F_27(x), F_23(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_15(x)*F_23(x))
Eq(F_30(x), F_31(x) + F_32(x) + F_42(x))
Eq(F_31(x), 0)
Eq(F_32(x), F_15(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), F_17(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_31(x) + F_32(x) + F_37(x))
Eq(F_37(x), F_15(x)*F_38(x))
Eq(F_38(x), F_17(x) + F_39(x))
Eq(F_39(x), F_31(x) + F_37(x) + F_40(x))
Eq(F_40(x), F_15(x)*F_41(x))
Eq(F_41(x), F_17(x) + F_39(x))
Eq(F_42(x), F_15(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_51(x))
Eq(F_44(x), F_17(x) + F_45(x))
Eq(F_45(x), F_31(x) + F_46(x) + F_50(x))
Eq(F_46(x), F_15(x)*F_47(x))
Eq(F_47(x), F_15(x) + F_48(x))
Eq(F_48(x), F_31(x) + F_46(x) + F_49(x))
Eq(F_49(x), F_15(x)*F_17(x))
Eq(F_50(x), F_15(x)*F_44(x))
Eq(F_51(x), F_39(x) + F_52(x))
Eq(F_52(x), 2*F_31(x) + F_53(x) + F_58(x))
Eq(F_53(x), F_15(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_49(x))
Eq(F_56(x), 2*F_31(x) + F_53(x) + F_57(x))
Eq(F_57(x), F_15(x)*F_39(x))
Eq(F_58(x), F_15(x)*F_51(x))
Eq(F_59(x), F_12(x)*F_15(x)*F_60(x))
Eq(F_60(x), F_1(x) + F_23(x))
Eq(F_61(x), F_15(x)*F_62(x))
Eq(F_62(x), F_63(x, 1))
Eq(F_63(x, k_0), F_1(x) + F_64(x, k_0) + F_66(x, k_0) + F_68(x, k_0))
Eq(F_64(x, k_0), F_63(x, k_0)*F_65(x, k_0))
Eq(F_65(x, k_0), k_0*x)
Eq(F_66(x, k_0), F_15(x)*F_67(x, k_0))
Eq(F_67(x, k_0), (-k_0*F_63(x, k_0) + F_63(x, 1))/(1 - k_0))
Eq(F_68(x, k_0), F_69(x, k_0))
Eq(F_69(x, k_0), F_15(x)*F_70(x, k_0))
Eq(F_70(x, k_0), F_141(x, k_0) + F_71(x, k_0))
Eq(F_71(x, k_0), F_7(x) + F_72(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0) + F_99(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0) + F_77(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0))
Eq(F_75(x, k_0), F_65(x, k_0)*F_76(x, k_0))
Eq(F_76(x, k_0), F_1(x) + F_74(x, k_0))
Eq(F_77(x, k_0), F_31(x) + F_78(x, k_0) + F_83(x, k_0))
Eq(F_78(x, k_0), F_65(x, k_0)*F_79(x, k_0))
Eq(F_79(x, k_0), F_17(x) + F_80(x, k_0))
Eq(F_80(x, k_0), F_31(x) + F_78(x, k_0) + F_81(x, k_0))
Eq(F_81(x, k_0), F_15(x)*F_82(x, k_0))
Eq(F_82(x, k_0), F_74(x, k_0) + F_80(x, k_0))
Eq(F_83(x, k_0), F_15(x)*F_84(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0) + F_92(x, k_0))
Eq(F_85(x, k_0), F_74(x, k_0) + F_86(x, k_0))
Eq(F_86(x, k_0), F_31(x) + F_87(x, k_0) + F_91(x, k_0))
Eq(F_87(x, k_0), F_65(x, k_0)*F_88(x, k_0))
Eq(F_88(x, k_0), F_15(x) + F_89(x, k_0))
Eq(F_89(x, k_0), F_31(x) + F_87(x, k_0) + F_90(x, k_0))
Eq(F_90(x, k_0), F_15(x)*F_74(x, k_0))
Eq(F_91(x, k_0), F_15(x)*F_85(x, k_0))
Eq(F_92(x, k_0), F_80(x, k_0) + F_93(x, k_0))
Eq(F_93(x, k_0), 2*F_31(x) + F_94(x, k_0) + F_98(x, k_0))
Eq(F_94(x, k_0), F_65(x, k_0)*F_95(x, k_0))
Eq(F_95(x, k_0), F_55(x) + F_96(x, k_0))
Eq(F_96(x, k_0), 2*F_31(x) + F_94(x, k_0) + F_97(x, k_0))
Eq(F_97(x, k_0), F_15(x)*F_80(x, k_0))
Eq(F_98(x, k_0), F_15(x)*F_92(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + F_110(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_104(x, k_0) + F_31(x))
Eq(F_101(x, k_0), F_102(x, k_0)*F_65(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0) + F_15(x))
Eq(F_103(x, k_0), F_90(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0)*F_15(x))
Eq(F_105(x, k_0), F_106(x, k_0) + F_107(x, k_0))
Eq(F_106(x, k_0), F_103(x, k_0) + F_74(x, k_0))
Eq(F_107(x, k_0), F_100(x, k_0) + F_108(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_100(x, k_0)*F_15(x))
Eq(F_110(x, k_0), F_111(x, k_0) + F_112(x, k_0) + F_125(x, k_0) + F_31(x))
Eq(F_111(x, k_0), 0)
Eq(F_112(x, k_0), F_113(x, k_0)*F_15(x))
Eq(F_113(x, k_0), F_114(x, k_0) + F_115(x, k_0))
Eq(F_114(x, k_0), F_80(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0))
Eq(F_116(x, k_0), F_111(x, k_0) + F_112(x, k_0) + F_117(x, k_0) + F_31(x))
Eq(F_117(x, k_0), F_118(x, k_0)*F_15(x))
Eq(F_118(x, k_0), F_119(x, k_0) + F_122(x, k_0))
Eq(F_119(x, k_0), F_120(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0)*F_15(x))
Eq(F_121(x, k_0), F_119(x, k_0) + F_74(x, k_0))
Eq(F_122(x, k_0), F_117(x, k_0) + F_123(x, k_0) + 2*F_31(x))
Eq(F_123(x, k_0), F_124(x, k_0)*F_15(x))
Eq(F_124(x, k_0), F_122(x, k_0) + F_80(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0)*F_15(x))
Eq(F_126(x, k_0), F_127(x, k_0) + F_134(x, k_0))
Eq(F_127(x, k_0), F_119(x, k_0) + F_128(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0) + F_133(x, k_0) + 2*F_31(x))
Eq(F_129(x, k_0), F_130(x, k_0)*F_15(x))
Eq(F_130(x, k_0), F_131(x, k_0) + F_89(x, k_0))
Eq(F_131(x, k_0), F_129(x, k_0) + F_132(x, k_0) + 2*F_31(x))
Eq(F_132(x, k_0), F_119(x, k_0)*F_15(x))
Eq(F_133(x, k_0), F_127(x, k_0)*F_15(x))
Eq(F_134(x, k_0), F_122(x, k_0) + F_135(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0) + F_140(x, k_0) + 3*F_31(x))
Eq(F_136(x, k_0), F_137(x, k_0)*F_15(x))
Eq(F_137(x, k_0), F_138(x, k_0) + F_96(x, k_0))
Eq(F_138(x, k_0), F_136(x, k_0) + F_139(x, k_0) + 3*F_31(x))
Eq(F_139(x, k_0), F_122(x, k_0)*F_15(x))
Eq(F_140(x, k_0), F_134(x, k_0)*F_15(x))
Eq(F_141(x, k_0), F_12(x)*F_142(x, k_0)*F_15(x))
Eq(F_142(x, k_0), F_143(x, k_0) + F_60(x))
Eq(F_143(x, k_0), F_100(x, k_0) + F_74(x, k_0))
Pack JSON:
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Specification JSON:
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