0123_0132_0321_1320
Counting sequence:
1, 1, 2, 6, 20, 64, 195, 571, 1622, 4505, 12310, 33247, 89049, 237090, 628528, 1661000, 4379332, 11526510, 30298955, 79567521, 208797502, 547612231, 1435613022, 3762373701, 9857800865, 25823613344, 67638206760, 177141340606, 463886480652, 1214719430540, 3180674467075, 8328109280327, 21805263990294, 57090903920085, 149473890225398, 391343651662955, 1024582834572697, 2682456391668670, 7022889419654960, 18386418025733556, 48136776974413892, 126024737531237386, 329939084886749067, 863795815663903021, 2261454959174737310, 5920582255999853699, 15500318197103902750, 40580425111870001041, 106241062691622381057, 278142974069229690300, 728188281728531772040, 1906422715541295775082, 4991081553745215835564, 13066825323394072279080, 34209401171836442078243, 89561391702914136089235, 234474800958503730435862, 613863065215792583689105, 1607114502775265077549590, 4207480659282784762771191, 11015327907418653438360857, 28838503927664304007477466, 75500185604956515494374512, 197662056345969756296221216, 517485990350481781035406980, 1354795928540533642092201254, 3546901822941235255805563915, 9285909595623404346453187001, 24310827074609442225811350462, 63646571849565851215495529535, 166628888916809969189704524830, 436240095786307771891676572637, 1142091400213000777561442200609, 2990034108394469422944883994200, 7828010932053957215577677659688, 20493998701934501672397084685590, 53653985202083746698831447741452, 140467956960985136218533001167940, 367749885794208457545639040958595, 962781700648313827596127092035551, 2520595216604080207598228175736022, 6599003950070621159909529316278221, 17276416635421172001552303535236982, 45230245959819672303591268813633411, 118414321251291399826909277953985625, 310012717808561637012512115144886134, 811623832203407730881378167673712880, 2124858778859689994973124588262244236, 5562952504491719132720999997884911492, 14563998734847581160555884206936178370, 38129043700515251863678670226010901195, 99823132367626629459944161677270978117, 261340353404221546575081885218150833054, 684197927848751830383157634801879011195, 1791253430149461584810103300836881067358, 4689562362614488204518576831007553807145, 12277433657723713589688476318783359465217, 32142738610616073686432550378537682685300, 84150782174243349713380571323220004654600, 220309607912351659941251956603902963272386, 576778041563286999085460884514050149012012
Generating function in Maple syntax:
(3*x^7-7*x^6+20*x^5-39*x^4+43*x^3-26*x^2+8*x-1)/(2*x-1)/(x^2-3*x+1)/(-1+x)^4
Generating function in latex syntax:
\frac{3 x^{7}-7 x^{6}+20 x^{5}-39 x^{4}+43 x^{3}-26 x^{2}+8 x -1}{\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(-1+x \right)^{4}}
Generating function in sympy syntax:
(3*x**7 - 7*x**6 + 20*x**5 - 39*x**4 + 43*x**3 - 26*x**2 + 8*x - 1)/((x - 1)**4*(2*x - 1)*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x^2-3*x+1)*(-1+x)^4*F(x)-3*x^7+7*x^6-20*x^5+39*x^4-43*x^3+26*x^2-8*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(-1+x \right)^{4} F \! \left(x \right)-3 x^{7}+7 x^{6}-20 x^{5}+39 x^{4}-43 x^{3}+26 x^{2}-8 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/30*(66*5^(1/2)-120)*(3/2-1/2*5^(1/2))^(-n)+1/30*(-66*5^(1/2)-120)*(3/2+1/2*5^(1/2))^(-n)-1/6*n^3+3/2*n^2-16/3*n-3*2^(n-1)+9)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(66 \sqrt{5}-120\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{30}+\frac{\left(-66 \sqrt{5}-120\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{30}-\frac{n^{3}}{6}+\frac{3 n^{2}}{2}\\-\frac{16 n}{3}-3 \,2^{n -1}+9 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 64
a(6) = 195
a(7) = 571
a(n+3) = -1/6*n^3+3/2*n^2+2*a(n)-7*a(n+1)+5*a(n+2)-10/3*n+4, n >= 8
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 20
a \! \left(5\right) = 64
a \! \left(6\right) = 195
a \! \left(7\right) = 571
a \! \left(n +3\right) = -\frac{n^{3}}{6}+\frac{3 n^{2}}{2}+2 a \! \left(n \right)-7 a \! \left(n +1\right)+5 a \! \left(n +2\right)-\frac{10 n}{3}+4, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14811/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[19,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[14,x]
F[12,x] = F[13,x]
F[13,x] = F[10,x]*F[4,x]
F[14,x] = F[15,x]+F[16,x]+F[18,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[4,x]
F[18,x] = F[12,x]*F[4,x]
F[19,x] = F[2,x]+F[20,x]
F[20,x] = F[15,x]+F[178,x]+F[21,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[34,x]
F[23,x] = F[24,x]+F[7,x]
F[24,x] = F[15,x]+F[25,x]+F[28,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[17,x]+F[27,x]
F[27,x] = F[14,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[11,x]+F[30,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[16,x]
F[32,x] = F[33,x]
F[33,x] = F[31,x]*F[4,x]
F[34,x] = F[20,x]+F[35,x]
F[35,x] = F[147,x]+F[15,x]+F[175,x]+F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]+F[46,x]
F[38,x] = F[24,x]+F[39,x]
F[39,x] = F[15,x]+F[40,x]+F[41,x]+F[44,x]
F[40,x] = 0
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[27,x]+F[43,x]
F[43,x] = F[32,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[30,x]
F[46,x] = F[35,x]+F[47,x]
F[47,x] = F[144,x]+F[15,x]+F[48,x]+F[77,x]+F[78,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[54,x]
F[50,x] = F[39,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[43,x]
F[54,x] = F[47,x]+F[55,x]
F[55,x] = F[15,x]+F[56,x]+F[60,x]+F[61,x]+F[62,x]+F[76,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[51,x]
F[59,x] = F[55,x]
F[60,x] = 0
F[61,x] = 0
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[65,x]
F[65,x] = 3*F[15,x]+F[66,x]+F[70,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[32,x]
F[69,x] = F[65,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]+F[75,x]
F[74,x] = F[31,x]
F[75,x] = F[71,x]
F[76,x] = 0
F[77,x] = 0
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[64,x]+F[80,x]
F[80,x] = F[81,x]
F[81,x] = 2*F[15,x]+F[82,x]+F[93,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[84,x]+F[86,x]
F[84,x] = F[14,x]+F[85,x]
F[85,x] = F[33,x]
F[86,x] = F[81,x]+F[87,x]
F[87,x] = 2*F[15,x]+F[70,x]+F[88,x]+F[92,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[85,x]
F[91,x] = F[87,x]
F[92,x] = 0
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[102,x]+F[97,x]
F[97,x] = F[12,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[4,x]
F[100,x] = F[101,x]+F[17,x]
F[101,x] = F[16,x]
F[102,x] = F[103,x]+F[94,x]
F[103,x] = 2*F[15,x]+F[104,x]+F[124,x]
F[104,x] = F[105,x]*F[4,x]
F[105,x] = F[106,x]+F[110,x]
F[106,x] = F[107,x]+F[98,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]*F[4,x]
F[109,x] = F[101,x]
F[110,x] = F[103,x]+F[111,x]
F[111,x] = 2*F[15,x]+F[112,x]+F[116,x]+F[117,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[114,x]+F[115,x]
F[114,x] = F[107,x]
F[115,x] = F[111,x]
F[116,x] = 0
F[117,x] = F[118,x]*F[4,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[123,x]
F[122,x] = F[16,x]
F[123,x] = F[120,x]
F[124,x] = F[125,x]*F[4,x]
F[125,x] = F[119,x]+F[126,x]
F[126,x] = F[127,x]
F[127,x] = F[128,x]
F[128,x] = F[129,x]*F[4,x]
F[129,x] = F[130,x]+F[132,x]
F[130,x] = F[131,x]+F[4,x]
F[131,x] = F[99,x]
F[132,x] = F[127,x]+F[133,x]
F[133,x] = 2*F[15,x]+F[124,x]+F[134,x]
F[134,x] = F[135,x]*F[4,x]
F[135,x] = F[136,x]+F[138,x]
F[136,x] = F[131,x]+F[137,x]
F[137,x] = F[108,x]
F[138,x] = F[133,x]+F[139,x]
F[139,x] = 2*F[15,x]+F[116,x]+F[117,x]+F[140,x]
F[140,x] = F[141,x]*F[4,x]
F[141,x] = F[142,x]+F[143,x]
F[142,x] = F[137,x]
F[143,x] = F[139,x]
F[144,x] = F[145,x]*F[4,x]
F[145,x] = F[146,x]
F[146,x] = F[65,x]+F[71,x]
F[147,x] = F[148,x]*F[4,x]
F[148,x] = F[149,x]+F[80,x]
F[149,x] = F[150,x]
F[150,x] = F[15,x]+F[151,x]+F[174,x]
F[151,x] = F[152,x]*F[4,x]
F[152,x] = F[153,x]+F[155,x]
F[153,x] = F[154,x]+F[4,x]
F[154,x] = F[15,x]+F[18,x]+F[25,x]
F[155,x] = F[150,x]+F[156,x]
F[156,x] = F[147,x]+F[15,x]+F[157,x]+F[93,x]
F[157,x] = F[158,x]*F[4,x]
F[158,x] = F[159,x]+F[161,x]
F[159,x] = F[154,x]+F[160,x]
F[160,x] = F[15,x]+F[33,x]+F[40,x]+F[41,x]
F[161,x] = F[156,x]+F[162,x]
F[162,x] = F[15,x]+F[163,x]+F[70,x]+F[77,x]+F[78,x]
F[163,x] = F[164,x]*F[4,x]
F[164,x] = F[165,x]+F[167,x]
F[165,x] = F[160,x]+F[166,x]
F[166,x] = F[52,x]
F[167,x] = F[162,x]+F[168,x]
F[168,x] = F[15,x]+F[169,x]+F[173,x]+F[60,x]+F[61,x]+F[62,x]
F[169,x] = F[170,x]*F[4,x]
F[170,x] = F[171,x]+F[172,x]
F[171,x] = F[166,x]
F[172,x] = F[168,x]
F[173,x] = 0
F[174,x] = F[2,x]*F[4,x]
F[175,x] = F[176,x]*F[4,x]
F[176,x] = F[146,x]+F[177,x]
F[177,x] = F[81,x]+F[94,x]
F[178,x] = F[179,x]*F[4,x]
F[179,x] = F[177,x]+F[180,x]
F[180,x] = F[150,x]+F[2,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_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{19}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{14}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{18}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right)+F_{178}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{34}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{7}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right)+F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{17}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{14}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{16}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{20}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{147}\! \left(x \right)+F_{15}\! \left(x \right)+F_{175}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{46}\! \left(x \right)
F_{38}\! \left(x \right) = F_{24}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{15}\! \left(x \right)+F_{40}\! \left(x \right)+F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{40}\! \left(x \right) = 0
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{27}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{32}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{30}\! \left(x \right)
F_{46}\! \left(x \right) = F_{35}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{144}\! \left(x \right)+F_{15}\! \left(x \right)+F_{48}\! \left(x \right)+F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{54}\! \left(x \right)
F_{50}\! \left(x \right) = F_{39}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{43}\! \left(x \right)
F_{54}\! \left(x \right) = F_{47}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{15}\! \left(x \right)+F_{56}\! \left(x \right)+F_{60}\! \left(x \right)+F_{61}\! \left(x \right)+F_{62}\! \left(x \right)+F_{76}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{51}\! \left(x \right)
F_{59}\! \left(x \right) = F_{55}\! \left(x \right)
F_{60}\! \left(x \right) = 0
F_{61}\! \left(x \right) = 0
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{66}\! \left(x \right)+F_{70}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \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_{32}\! \left(x \right)
F_{69}\! \left(x \right) = F_{65}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{75}\! \left(x \right)
F_{74}\! \left(x \right) = F_{31}\! \left(x \right)
F_{75}\! \left(x \right) = F_{71}\! \left(x \right)
F_{76}\! \left(x \right) = 0
F_{77}\! \left(x \right) = 0
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{64}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{82}\! \left(x \right)+F_{93}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{86}\! \left(x \right)
F_{84}\! \left(x \right) = F_{14}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{33}\! \left(x \right)
F_{86}\! \left(x \right) = F_{81}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{70}\! \left(x \right)+F_{88}\! \left(x \right)+F_{92}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{85}\! \left(x \right)
F_{91}\! \left(x \right) = F_{87}\! \left(x \right)
F_{92}\! \left(x \right) = 0
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{102}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{12}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{4}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{17}\! \left(x \right)
F_{101}\! \left(x \right) = F_{16}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{94}\! \left(x \right)
F_{103}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{104}\! \left(x \right)+F_{124}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{4}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{110}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{98}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{101}\! \left(x \right)
F_{110}\! \left(x \right) = F_{103}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{112}\! \left(x \right)+F_{116}\! \left(x \right)+F_{117}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{115}\! \left(x \right)
F_{114}\! \left(x \right) = F_{107}\! \left(x \right)
F_{115}\! \left(x \right) = F_{111}\! \left(x \right)
F_{116}\! \left(x \right) = 0
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{4}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{123}\! \left(x \right)
F_{122}\! \left(x \right) = F_{16}\! \left(x \right)
F_{123}\! \left(x \right) = F_{120}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{4}\! \left(x \right)
F_{125}\! \left(x \right) = F_{119}\! \left(x \right)+F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{4}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{132}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{4}\! \left(x \right)
F_{131}\! \left(x \right) = F_{99}\! \left(x \right)
F_{132}\! \left(x \right) = F_{127}\! \left(x \right)+F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{124}\! \left(x \right)+F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{4}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{138}\! \left(x \right)
F_{136}\! \left(x \right) = F_{131}\! \left(x \right)+F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{108}\! \left(x \right)
F_{138}\! \left(x \right) = F_{133}\! \left(x \right)+F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{116}\! \left(x \right)+F_{117}\! \left(x \right)+F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{4}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{143}\! \left(x \right)
F_{142}\! \left(x \right) = F_{137}\! \left(x \right)
F_{143}\! \left(x \right) = F_{139}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right) F_{4}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{65}\! \left(x \right)+F_{71}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{4}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{80}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{15}\! \left(x \right)+F_{151}\! \left(x \right)+F_{174}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{4}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{155}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{4}\! \left(x \right)
F_{154}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)+F_{25}\! \left(x \right)
F_{155}\! \left(x \right) = F_{150}\! \left(x \right)+F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{147}\! \left(x \right)+F_{15}\! \left(x \right)+F_{157}\! \left(x \right)+F_{93}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right) F_{4}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{161}\! \left(x \right)
F_{159}\! \left(x \right) = F_{154}\! \left(x \right)+F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{15}\! \left(x \right)+F_{33}\! \left(x \right)+F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{161}\! \left(x \right) = F_{156}\! \left(x \right)+F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{15}\! \left(x \right)+F_{163}\! \left(x \right)+F_{70}\! \left(x \right)+F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right) F_{4}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)+F_{167}\! \left(x \right)
F_{165}\! \left(x \right) = F_{160}\! \left(x \right)+F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{52}\! \left(x \right)
F_{167}\! \left(x \right) = F_{162}\! \left(x \right)+F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{15}\! \left(x \right)+F_{169}\! \left(x \right)+F_{173}\! \left(x \right)+F_{60}\! \left(x \right)+F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right) F_{4}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)+F_{172}\! \left(x \right)
F_{171}\! \left(x \right) = F_{166}\! \left(x \right)
F_{172}\! \left(x \right) = F_{168}\! \left(x \right)
F_{173}\! \left(x \right) = 0
F_{174}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right) F_{4}\! \left(x \right)
F_{176}\! \left(x \right) = F_{146}\! \left(x \right)+F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = F_{81}\! \left(x \right)+F_{94}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right) F_{4}\! \left(x \right)
F_{179}\! \left(x \right) = F_{177}\! \left(x \right)+F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{150}\! \left(x \right)+F_{2}\! \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_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_19(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_14(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_10(x)*F_4(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_18(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_4(x))
Eq(F_18(x), F_12(x)*F_4(x))
Eq(F_19(x), F_2(x) + F_20(x))
Eq(F_20(x), F_15(x) + F_178(x) + F_21(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_34(x))
Eq(F_23(x), F_24(x) + F_7(x))
Eq(F_24(x), F_15(x) + F_25(x) + F_28(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_17(x) + F_27(x))
Eq(F_27(x), F_14(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_11(x) + F_30(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_16(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_31(x)*F_4(x))
Eq(F_34(x), F_20(x) + F_35(x))
Eq(F_35(x), F_147(x) + F_15(x) + F_175(x) + F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_46(x))
Eq(F_38(x), F_24(x) + F_39(x))
Eq(F_39(x), F_15(x) + F_40(x) + F_41(x) + F_44(x))
Eq(F_40(x), 0)
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_27(x) + F_43(x))
Eq(F_43(x), F_32(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_30(x))
Eq(F_46(x), F_35(x) + F_47(x))
Eq(F_47(x), F_144(x) + F_15(x) + F_48(x) + F_77(x) + F_78(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_54(x))
Eq(F_50(x), F_39(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_43(x))
Eq(F_54(x), F_47(x) + F_55(x))
Eq(F_55(x), F_15(x) + F_56(x) + F_60(x) + F_61(x) + F_62(x) + F_76(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_51(x))
Eq(F_59(x), F_55(x))
Eq(F_60(x), 0)
Eq(F_61(x), 0)
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), 3*F_15(x) + F_66(x) + F_70(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_32(x))
Eq(F_69(x), F_65(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_75(x))
Eq(F_74(x), F_31(x))
Eq(F_75(x), F_71(x))
Eq(F_76(x), 0)
Eq(F_77(x), 0)
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_64(x) + F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), 2*F_15(x) + F_82(x) + F_93(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_86(x))
Eq(F_84(x), F_14(x) + F_85(x))
Eq(F_85(x), F_33(x))
Eq(F_86(x), F_81(x) + F_87(x))
Eq(F_87(x), 2*F_15(x) + F_70(x) + F_88(x) + F_92(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_85(x))
Eq(F_91(x), F_87(x))
Eq(F_92(x), 0)
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(x), F_102(x) + F_97(x))
Eq(F_97(x), F_12(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_4(x))
Eq(F_100(x), F_101(x) + F_17(x))
Eq(F_101(x), F_16(x))
Eq(F_102(x), F_103(x) + F_94(x))
Eq(F_103(x), F_104(x) + F_124(x) + 2*F_15(x))
Eq(F_104(x), F_105(x)*F_4(x))
Eq(F_105(x), F_106(x) + F_110(x))
Eq(F_106(x), F_107(x) + F_98(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x)*F_4(x))
Eq(F_109(x), F_101(x))
Eq(F_110(x), F_103(x) + F_111(x))
Eq(F_111(x), F_112(x) + F_116(x) + F_117(x) + 2*F_15(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_114(x) + F_115(x))
Eq(F_114(x), F_107(x))
Eq(F_115(x), F_111(x))
Eq(F_116(x), 0)
Eq(F_117(x), F_118(x)*F_4(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x)*F_4(x))
Eq(F_121(x), F_122(x) + F_123(x))
Eq(F_122(x), F_16(x))
Eq(F_123(x), F_120(x))
Eq(F_124(x), F_125(x)*F_4(x))
Eq(F_125(x), F_119(x) + F_126(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_129(x)*F_4(x))
Eq(F_129(x), F_130(x) + F_132(x))
Eq(F_130(x), F_131(x) + F_4(x))
Eq(F_131(x), F_99(x))
Eq(F_132(x), F_127(x) + F_133(x))
Eq(F_133(x), F_124(x) + F_134(x) + 2*F_15(x))
Eq(F_134(x), F_135(x)*F_4(x))
Eq(F_135(x), F_136(x) + F_138(x))
Eq(F_136(x), F_131(x) + F_137(x))
Eq(F_137(x), F_108(x))
Eq(F_138(x), F_133(x) + F_139(x))
Eq(F_139(x), F_116(x) + F_117(x) + F_140(x) + 2*F_15(x))
Eq(F_140(x), F_141(x)*F_4(x))
Eq(F_141(x), F_142(x) + F_143(x))
Eq(F_142(x), F_137(x))
Eq(F_143(x), F_139(x))
Eq(F_144(x), F_145(x)*F_4(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_65(x) + F_71(x))
Eq(F_147(x), F_148(x)*F_4(x))
Eq(F_148(x), F_149(x) + F_80(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_15(x) + F_151(x) + F_174(x))
Eq(F_151(x), F_152(x)*F_4(x))
Eq(F_152(x), F_153(x) + F_155(x))
Eq(F_153(x), F_154(x) + F_4(x))
Eq(F_154(x), F_15(x) + F_18(x) + F_25(x))
Eq(F_155(x), F_150(x) + F_156(x))
Eq(F_156(x), F_147(x) + F_15(x) + F_157(x) + F_93(x))
Eq(F_157(x), F_158(x)*F_4(x))
Eq(F_158(x), F_159(x) + F_161(x))
Eq(F_159(x), F_154(x) + F_160(x))
Eq(F_160(x), F_15(x) + F_33(x) + F_40(x) + F_41(x))
Eq(F_161(x), F_156(x) + F_162(x))
Eq(F_162(x), F_15(x) + F_163(x) + F_70(x) + F_77(x) + F_78(x))
Eq(F_163(x), F_164(x)*F_4(x))
Eq(F_164(x), F_165(x) + F_167(x))
Eq(F_165(x), F_160(x) + F_166(x))
Eq(F_166(x), F_52(x))
Eq(F_167(x), F_162(x) + F_168(x))
Eq(F_168(x), F_15(x) + F_169(x) + F_173(x) + F_60(x) + F_61(x) + F_62(x))
Eq(F_169(x), F_170(x)*F_4(x))
Eq(F_170(x), F_171(x) + F_172(x))
Eq(F_171(x), F_166(x))
Eq(F_172(x), F_168(x))
Eq(F_173(x), 0)
Eq(F_174(x), F_2(x)*F_4(x))
Eq(F_175(x), F_176(x)*F_4(x))
Eq(F_176(x), F_146(x) + F_177(x))
Eq(F_177(x), F_81(x) + F_94(x))
Eq(F_178(x), F_179(x)*F_4(x))
Eq(F_179(x), F_177(x) + F_180(x))
Eq(F_180(x), F_150(x) + F_2(x))
Pack JSON:
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Specification JSON:
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