0123_0132_0213_0231_1230
Counting sequence:
1, 1, 2, 6, 19, 62, 206, 694, 2367, 8166, 28474, 100264, 356214, 1275740, 4601884, 16707058, 61004111, 223899142, 825567074, 3056756608, 11360715506, 42367889332, 158497811684, 594634566508, 2236744486694, 8433980266972, 31872742965636, 120699715205424, 457962285475852, 1740736347334648, 6627730519097784, 25274285039490602, 96523492641127663, 369138193799954374, 1413551949592251122, 5419626939074937168, 20803311259633736538, 79941810229023292868, 307516921180672183700, 1184116880535505945908, 4563828712548130510306, 17605710140449548345332, 67974941231071478156684, 262662528496067236106608, 1015746759976509988004276, 3930935588552703360397192, 15223539568971506520794504, 58997218802813736010723828, 228787022727077315325376646, 887776592116924173142869916, 3446971070332422694216229684, 13391309683271909166884436544, 52053548221029809615147176244, 202446575965789990751151589000, 787761564600120005045037802472, 3066869515189675263338095501528, 11945499239080910109708327570668, 46549448785704794282143764397048, 181475967721469684105157378783560, 707801529966031523312600492066272, 2761756934064662811412525962998936, 10780404952573590681826636611970288, 42097347527506396848014331638483312, 164451963374498330444316302132792986, 642662489192861334558396682053325871, 2512357976426022669042598708919407942, 9824944595969705782668597443744873234, 38434768459352722154829701374845651568, 150404122975964053915225752418507060586, 588752081021471665239807993656739727972, 2305358714330348565127952655746047638644, 9029717740871928847757642400441196236388, 35378210854772694165258465321796805031626, 138650088340445355817126293455009074136452, 543530267257129264429141978922399353956284, 2131294430549654302510540419531375837127408, 8359422206296229010809122228850288210403236, 32795876523256465239056557417917268763765992, 128697344496255032344093384566481198962002024, 505154918738997340448726424476882376642610588, 1983269074719407644408679676524940488777159106, 7788220522029304692994245255097791595744342452, 30590879981245233187005830812505563460118107644, 120182297249943612581038545699782409391224765568, 472260460946010041349392038840390027181658530076, 1856149954805152553917421181391227433992137879192, 7296806444190775633056335655485224624067603925304, 28690549595774328859623555407728637160172838877928, 112831206336860401943924052640277021445728298931796, 443815056022238678677410089329032202037878846401672, 1746045043296708767334844750809232260293306083093944, 6870489866367654588906307276020137512495464820534688, 27039403411399774128838799116853297668873555676523176, 106434395248188942095796797722000875981164976888791952, 419025814500813594586368984714363639979070826472524304, 1649954250436779410536295954382882156385138489788584708, 6497912610834480563275135192496513094015698238136496966, 25594415507853196488469885112320737606584234407648840732, 100828786783073140127358523290200517392064170705069516564, 397274303518857341541451380024878526549533958391237583008, 1565531063386033643712520599435599760828576010101774969956
Generating function in Maple syntax:
((2*x^2-5*x+2)*(1-4*x)^(1/2)+2*x^3-6*x^2+7*x-2)/(4*x^2-2*x)
Generating function in latex syntax:
\frac{\left(2 x^{2}-5 x +2\right) \sqrt{1-4 x}+2 x^{3}-6 x^{2}+7 x -2}{4 x^{2}-2 x}
Generating function in sympy syntax:
(2*x**3 - 6*x**2 + 7*x + sqrt(1 - 4*x)*(2*x**2 - 5*x + 2) - 2)/(4*x**2 - 2*x)
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*F(x)^2-(2*x-1)*(2*x^3-6*x^2+7*x-2)*F(x)+x^5-2*x^4-5*x^3+15*x^2-10*x+2 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} F \! \left(x \right)^{2}-\left(2 x -1\right) \left(2 x^{3}-6 x^{2}+7 x -2\right) F \! \left(x \right)+x^{5}-2 x^{4}-5 x^{3}+15 x^{2}-10 x +2 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 62
a(n+4) = -4*(-1+2*n)/(n+5)*a(n)+2*(15+13*n)/(n+5)*a(1+n)-(59+24*n)/(n+5)*a(n+2)+1/2*(63+17*n)/(n+5)*a(n+3), n >= 6
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) = 62
a \! \left(n +4\right) = -\frac{4 \left(-1+2 n \right) a \! \left(n \right)}{n +5}+\frac{2 \left(15+13 n \right) a \! \left(1+n \right)}{n +5}-\frac{\left(59+24 n \right) a \! \left(n +2\right)}{n +5}+\frac{\left(63+17 n \right) a \! \left(n +3\right)}{10+2 n}, \quad n \geq 6
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21478/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[11,x]*F[3,x]
F[3,x] = F[1,x]+F[130,x]+F[4,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[7,x,k[0]]+F[9,x,k[0]]
F[7,x,k[0]] = F[6,x,k[0]]*F[8,x,k[0]]
F[8,x,k[0]] = k[0]*x
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[11,x] = x
F[12,x,k[0]] = F[11,x]*F[13,x,k[0]]
F[13,x,k[0]] = F[14,x]+F[63,x,k[0]]
F[14,x] = F[15,x]+F[28,x]
F[15,x] = F[16,x]+F[27,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[11,x]*F[19,x]
F[19,x] = F[20,x]+F[21,x]
F[20,x] = F[1,x]+F[11,x]
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[23,x]
F[23,x] = F[11,x]*F[24,x]
F[24,x] = F[1,x]+F[22,x]
F[25,x] = F[26,x]
F[26,x] = F[11,x]*F[22,x]
F[27,x] = F[11,x]
F[28,x] = F[29,x]+F[62,x]
F[29,x] = F[30,x]+F[41,x]
F[30,x] = F[31,x]
F[31,x] = F[11,x]*F[32,x]
F[32,x] = F[20,x]+F[33,x]
F[33,x] = F[30,x]+F[34,x]
F[34,x] = F[35,x]+F[36,x]+F[40,x]
F[35,x] = 0
F[36,x] = F[11,x]*F[37,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[11,x]
F[39,x] = F[34,x]
F[40,x] = F[11,x]*F[30,x]
F[41,x] = F[35,x]+F[42,x]+F[46,x]
F[42,x] = F[11,x]*F[43,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = F[17,x]
F[45,x] = F[41,x]
F[46,x] = F[11,x]*F[47,x]
F[47,x] = F[48,x]+F[52,x]
F[48,x] = F[22,x]+F[49,x]
F[49,x] = F[26,x]+F[35,x]+F[50,x]
F[50,x] = F[11,x]*F[51,x]
F[51,x] = F[11,x]+F[49,x]
F[52,x] = F[53,x]+F[58,x]
F[53,x] = F[35,x]+F[54,x]+F[56,x]
F[54,x] = F[11,x]*F[55,x]
F[55,x] = F[22,x]+F[53,x]
F[56,x] = F[11,x]*F[57,x]
F[57,x] = F[22,x]+F[53,x]
F[58,x] = 2*F[35,x]+F[59,x]+F[61,x]
F[59,x] = F[11,x]*F[60,x]
F[60,x] = F[25,x]+F[58,x]
F[61,x] = F[11,x]*F[53,x]
F[62,x] = F[34,x]
F[63,x,k[0]] = F[64,x,k[0]]+F[90,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]+F[89,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]+F[69,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]*F[8,x,k[0]]
F[68,x,k[0]] = F[1,x]+F[66,x,k[0]]
F[69,x,k[0]] = F[35,x]+F[70,x,k[0]]+F[72,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]*F[8,x,k[0]]
F[71,x,k[0]] = F[17,x]+F[69,x,k[0]]
F[72,x,k[0]] = F[11,x]*F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]+F[79,x,k[0]]
F[74,x,k[0]] = F[66,x,k[0]]+F[75,x,k[0]]
F[75,x,k[0]] = F[35,x]+F[76,x,k[0]]+F[78,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]*F[8,x,k[0]]
F[77,x,k[0]] = F[11,x]+F[75,x,k[0]]
F[78,x,k[0]] = F[11,x]*F[66,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]+F[85,x,k[0]]
F[80,x,k[0]] = F[35,x]+F[81,x,k[0]]+F[83,x,k[0]]
F[81,x,k[0]] = F[8,x,k[0]]*F[82,x,k[0]]
F[82,x,k[0]] = F[22,x]+F[80,x,k[0]]
F[83,x,k[0]] = F[11,x]*F[84,x,k[0]]
F[84,x,k[0]] = F[66,x,k[0]]+F[80,x,k[0]]
F[85,x,k[0]] = 2*F[35,x]+F[86,x,k[0]]+F[88,x,k[0]]
F[86,x,k[0]] = F[8,x,k[0]]*F[87,x,k[0]]
F[87,x,k[0]] = F[25,x]+F[85,x,k[0]]
F[88,x,k[0]] = F[11,x]*F[80,x,k[0]]
F[89,x,k[0]] = F[75,x,k[0]]
F[90,x,k[0]] = F[129,x,k[0]]+F[91,x,k[0]]
F[91,x,k[0]] = F[103,x,k[0]]+F[92,x,k[0]]
F[92,x,k[0]] = F[35,x]+F[76,x,k[0]]+F[93,x,k[0]]
F[93,x,k[0]] = F[11,x]*F[94,x,k[0]]
F[94,x,k[0]] = F[74,x,k[0]]+F[95,x,k[0]]
F[95,x,k[0]] = F[92,x,k[0]]+F[96,x,k[0]]
F[96,x,k[0]] = F[102,x,k[0]]+F[35,x]+F[97,x,k[0]]+F[98,x,k[0]]
F[97,x,k[0]] = 0
F[98,x,k[0]] = F[11,x]*F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]+F[101,x,k[0]]
F[100,x,k[0]] = F[75,x,k[0]]
F[101,x,k[0]] = F[96,x,k[0]]
F[102,x,k[0]] = F[11,x]*F[92,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]+F[105,x,k[0]]+F[109,x,k[0]]+F[35,x]
F[104,x,k[0]] = 0
F[105,x,k[0]] = F[106,x,k[0]]*F[11,x]
F[106,x,k[0]] = F[107,x,k[0]]+F[108,x,k[0]]
F[107,x,k[0]] = F[69,x,k[0]]
F[108,x,k[0]] = F[103,x,k[0]]
F[109,x,k[0]] = F[11,x]*F[110,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]+F[119,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[115,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]
F[113,x,k[0]] = F[11,x]*F[114,x,k[0]]
F[114,x,k[0]] = F[112,x,k[0]]+F[66,x,k[0]]
F[115,x,k[0]] = 2*F[35,x]+F[116,x,k[0]]+F[118,x,k[0]]
F[116,x,k[0]] = F[11,x]*F[117,x,k[0]]
F[117,x,k[0]] = F[115,x,k[0]]+F[75,x,k[0]]
F[118,x,k[0]] = F[11,x]*F[112,x,k[0]]
F[119,x,k[0]] = F[120,x,k[0]]+F[125,x,k[0]]
F[120,x,k[0]] = 2*F[35,x]+F[121,x,k[0]]+F[123,x,k[0]]
F[121,x,k[0]] = F[11,x]*F[122,x,k[0]]
F[122,x,k[0]] = F[120,x,k[0]]+F[80,x,k[0]]
F[123,x,k[0]] = F[11,x]*F[124,x,k[0]]
F[124,x,k[0]] = F[112,x,k[0]]+F[120,x,k[0]]
F[125,x,k[0]] = 3*F[35,x]+F[126,x,k[0]]+F[128,x,k[0]]
F[126,x,k[0]] = F[11,x]*F[127,x,k[0]]
F[127,x,k[0]] = F[125,x,k[0]]+F[85,x,k[0]]
F[128,x,k[0]] = F[11,x]*F[120,x,k[0]]
F[129,x,k[0]] = F[96,x,k[0]]
F[130,x] = F[11,x]*F[14,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_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{130}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{7}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = y x
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{10}\! \left(x , y\right) = \frac{F_{6}\! \left(x , y\right) y -F_{6}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{63}\! \left(x , y\right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{28}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{27}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{11}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right) F_{22}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{62}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{41}\! \left(x \right)
F_{30}\! \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_{20}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{30}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{35}\! \left(x \right) = 0
F_{36}\! \left(x \right) = F_{11}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{11}\! \left(x \right)
F_{39}\! \left(x \right) = F_{34}\! \left(x \right)
F_{40}\! \left(x \right) = F_{11}\! \left(x \right) F_{30}\! \left(x \right)
F_{41}\! \left(x \right) = F_{35}\! \left(x \right)+F_{42}\! \left(x \right)+F_{46}\! \left(x \right)
F_{42}\! \left(x \right) = F_{11}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{17}\! \left(x \right)
F_{45}\! \left(x \right) = F_{41}\! \left(x \right)
F_{46}\! \left(x \right) = F_{11}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{52}\! \left(x \right)
F_{48}\! \left(x \right) = F_{22}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{26}\! \left(x \right)+F_{35}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{11}\! \left(x \right)+F_{49}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{58}\! \left(x \right)
F_{53}\! \left(x \right) = F_{35}\! \left(x \right)+F_{54}\! \left(x \right)+F_{56}\! \left(x \right)
F_{54}\! \left(x \right) = F_{11}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{22}\! \left(x \right)+F_{53}\! \left(x \right)
F_{56}\! \left(x \right) = F_{11}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{22}\! \left(x \right)+F_{53}\! \left(x \right)
F_{58}\! \left(x \right) = 2 F_{35}\! \left(x \right)+F_{59}\! \left(x \right)+F_{61}\! \left(x \right)
F_{59}\! \left(x \right) = F_{11}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{25}\! \left(x \right)+F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{11}\! \left(x \right) F_{53}\! \left(x \right)
F_{62}\! \left(x \right) = F_{34}\! \left(x \right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{66}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{35}\! \left(x \right)+F_{70}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{69}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{35}\! \left(x \right)+F_{76}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{75}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{35}\! \left(x \right)+F_{81}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{80}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = 2 F_{35}\! \left(x \right)+F_{86}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{85}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{75}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{35}\! \left(x \right)+F_{76}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{92}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{35}\! \left(x \right)+F_{97}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = 0
F_{98}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{101}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{75}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{105}\! \left(x , y\right)+F_{109}\! \left(x , y\right)+F_{35}\! \left(x \right)
F_{104}\! \left(x , y\right) = 0
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{108}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{103}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{119}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = 2 F_{35}\! \left(x \right)+F_{116}\! \left(x , y\right)+F_{118}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{117}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{112}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{125}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = 2 F_{35}\! \left(x \right)+F_{121}\! \left(x , y\right)+F_{123}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{122}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{120}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = 3 F_{35}\! \left(x \right)+F_{126}\! \left(x , y\right)+F_{128}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{127}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{120}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{130}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \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_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_130(x) + F_4(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_12(x, k_0) + F_7(x, k_0) + F_9(x, k_0))
Eq(F_7(x, k_0), F_6(x, k_0)*F_8(x, k_0))
Eq(F_8(x, k_0), k_0*x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x))
Eq(F_10(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_11(x)*F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x) + F_63(x, k_0))
Eq(F_14(x), F_15(x) + F_28(x))
Eq(F_15(x), F_16(x) + F_27(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_11(x)*F_19(x))
Eq(F_19(x), F_20(x) + F_21(x))
Eq(F_20(x), F_1(x) + F_11(x))
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_11(x)*F_24(x))
Eq(F_24(x), F_1(x) + F_22(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_11(x)*F_22(x))
Eq(F_27(x), F_11(x))
Eq(F_28(x), F_29(x) + F_62(x))
Eq(F_29(x), F_30(x) + F_41(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_11(x)*F_32(x))
Eq(F_32(x), F_20(x) + F_33(x))
Eq(F_33(x), F_30(x) + F_34(x))
Eq(F_34(x), F_35(x) + F_36(x) + F_40(x))
Eq(F_35(x), 0)
Eq(F_36(x), F_11(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_11(x))
Eq(F_39(x), F_34(x))
Eq(F_40(x), F_11(x)*F_30(x))
Eq(F_41(x), F_35(x) + F_42(x) + F_46(x))
Eq(F_42(x), F_11(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), F_17(x))
Eq(F_45(x), F_41(x))
Eq(F_46(x), F_11(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_52(x))
Eq(F_48(x), F_22(x) + F_49(x))
Eq(F_49(x), F_26(x) + F_35(x) + F_50(x))
Eq(F_50(x), F_11(x)*F_51(x))
Eq(F_51(x), F_11(x) + F_49(x))
Eq(F_52(x), F_53(x) + F_58(x))
Eq(F_53(x), F_35(x) + F_54(x) + F_56(x))
Eq(F_54(x), F_11(x)*F_55(x))
Eq(F_55(x), F_22(x) + F_53(x))
Eq(F_56(x), F_11(x)*F_57(x))
Eq(F_57(x), F_22(x) + F_53(x))
Eq(F_58(x), 2*F_35(x) + F_59(x) + F_61(x))
Eq(F_59(x), F_11(x)*F_60(x))
Eq(F_60(x), F_25(x) + F_58(x))
Eq(F_61(x), F_11(x)*F_53(x))
Eq(F_62(x), F_34(x))
Eq(F_63(x, k_0), F_64(x, k_0) + F_90(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0) + F_89(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0) + F_69(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0)*F_8(x, k_0))
Eq(F_68(x, k_0), F_1(x) + F_66(x, k_0))
Eq(F_69(x, k_0), F_35(x) + F_70(x, k_0) + F_72(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0)*F_8(x, k_0))
Eq(F_71(x, k_0), F_17(x) + F_69(x, k_0))
Eq(F_72(x, k_0), F_11(x)*F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0) + F_79(x, k_0))
Eq(F_74(x, k_0), F_66(x, k_0) + F_75(x, k_0))
Eq(F_75(x, k_0), F_35(x) + F_76(x, k_0) + F_78(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0)*F_8(x, k_0))
Eq(F_77(x, k_0), F_11(x) + F_75(x, k_0))
Eq(F_78(x, k_0), F_11(x)*F_66(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0) + F_85(x, k_0))
Eq(F_80(x, k_0), F_35(x) + F_81(x, k_0) + F_83(x, k_0))
Eq(F_81(x, k_0), F_8(x, k_0)*F_82(x, k_0))
Eq(F_82(x, k_0), F_22(x) + F_80(x, k_0))
Eq(F_83(x, k_0), F_11(x)*F_84(x, k_0))
Eq(F_84(x, k_0), F_66(x, k_0) + F_80(x, k_0))
Eq(F_85(x, k_0), 2*F_35(x) + F_86(x, k_0) + F_88(x, k_0))
Eq(F_86(x, k_0), F_8(x, k_0)*F_87(x, k_0))
Eq(F_87(x, k_0), F_25(x) + F_85(x, k_0))
Eq(F_88(x, k_0), F_11(x)*F_80(x, k_0))
Eq(F_89(x, k_0), F_75(x, k_0))
Eq(F_90(x, k_0), F_129(x, k_0) + F_91(x, k_0))
Eq(F_91(x, k_0), F_103(x, k_0) + F_92(x, k_0))
Eq(F_92(x, k_0), F_35(x) + F_76(x, k_0) + F_93(x, k_0))
Eq(F_93(x, k_0), F_11(x)*F_94(x, k_0))
Eq(F_94(x, k_0), F_74(x, k_0) + F_95(x, k_0))
Eq(F_95(x, k_0), F_92(x, k_0) + F_96(x, k_0))
Eq(F_96(x, k_0), F_102(x, k_0) + F_35(x) + F_97(x, k_0) + F_98(x, k_0))
Eq(F_97(x, k_0), 0)
Eq(F_98(x, k_0), F_11(x)*F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + F_101(x, k_0))
Eq(F_100(x, k_0), F_75(x, k_0))
Eq(F_101(x, k_0), F_96(x, k_0))
Eq(F_102(x, k_0), F_11(x)*F_92(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0) + F_105(x, k_0) + F_109(x, k_0) + F_35(x))
Eq(F_104(x, k_0), 0)
Eq(F_105(x, k_0), F_106(x, k_0)*F_11(x))
Eq(F_106(x, k_0), F_107(x, k_0) + F_108(x, k_0))
Eq(F_107(x, k_0), F_69(x, k_0))
Eq(F_108(x, k_0), F_103(x, k_0))
Eq(F_109(x, k_0), F_11(x)*F_110(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0) + F_119(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_115(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0))
Eq(F_113(x, k_0), F_11(x)*F_114(x, k_0))
Eq(F_114(x, k_0), F_112(x, k_0) + F_66(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0) + F_118(x, k_0) + 2*F_35(x))
Eq(F_116(x, k_0), F_11(x)*F_117(x, k_0))
Eq(F_117(x, k_0), F_115(x, k_0) + F_75(x, k_0))
Eq(F_118(x, k_0), F_11(x)*F_112(x, k_0))
Eq(F_119(x, k_0), F_120(x, k_0) + F_125(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0) + F_123(x, k_0) + 2*F_35(x))
Eq(F_121(x, k_0), F_11(x)*F_122(x, k_0))
Eq(F_122(x, k_0), F_120(x, k_0) + F_80(x, k_0))
Eq(F_123(x, k_0), F_11(x)*F_124(x, k_0))
Eq(F_124(x, k_0), F_112(x, k_0) + F_120(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0) + F_128(x, k_0) + 3*F_35(x))
Eq(F_126(x, k_0), F_11(x)*F_127(x, k_0))
Eq(F_127(x, k_0), F_125(x, k_0) + F_85(x, k_0))
Eq(F_128(x, k_0), F_11(x)*F_120(x, k_0))
Eq(F_129(x, k_0), F_96(x, k_0))
Eq(F_130(x), F_11(x)*F_14(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:
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