0123_0132_0213_1203_3012
Counting sequence:
1, 1, 2, 6, 19, 61, 197, 644, 2138, 7214, 24717, 85854, 301786, 1071753, 3839966, 13863663, 50386858, 184200465, 676868352, 2498687216, 9262037287, 34459728332, 128640208838, 481693283799, 1808755076320, 6809335147920, 25695539149067, 97176478811538, 368252616638812, 1398137761185713, 5317628928166468, 20258160511927721, 77294867815050082, 295344522699994003, 1130049367787726650, 4329343254982778804, 16606246966481228181, 63770109051178448086, 245150420418805924174, 943395096875338430285, 3633938696783629761878, 14010827013566890525792, 54067068579978472138089, 208817456206992816190560, 807140214468063537457448, 3122222045547219075241027, 12086390851955459309656754, 46820268800616477198073550, 181494229183208128595675883, 703997969406250696961928514, 2732425958103450113703386952, 10611657352844400057841523049, 41234988598964315468063553056, 160319731737076833391228105828, 623645271418221994356758750795, 2427221748308335264489912886714, 9451364229543477284948720592396, 36820124218017845582691374515801, 143507491808838753403588755455964, 559571658297658732812678352426212, 2182841654413495224869541568108991, 8518596276168432622438657324384426, 33257324709031434630332884659727832, 129889643585386991390219846083276046, 507486400427189458673850314910277515, 1983498766604724139148624670291038785, 7755187581716409673337381648336914449, 30331992797126731606972069038441037833, 118673422793243114271501175644629915681, 464457193078629303971898485524072628263, 1818333800293194403007156197695230980043, 7120875415507713290841211083759310699955, 27894677497090025286287423672518953161097, 109303472353029010858917932194632467029201, 428418137771512957419812648817705913191837, 1679653775189843402266283065387951242127557, 6586983965013556949876945631081712482316673, 25838384812582906115525829253549246786903249, 101380203458765617613764540530883424047531001, 397875526719803538608362854534835892905576439, 1561870064514372969694070120215739444381385779, 6132585560047232091311390426227217753522224727, 24084681062231045623808968187353945377632230845, 94609417705070151940545169350743677090640006931, 371724964791079538758261460309350533252547283935, 1460833644285643331963955235668902021923305489285, 5742081231593852487208270060859991447183932807099, 22574876007622648780268333599248303153751725286803, 88770137751422890903458545318083568605188442040581, 349133857228380909410611174735410632702119948959043, 1373405335194395667872972333103889884207087945689423, 5403627267702780466177483639823808379596692202645665, 21264255824588710759249383686169499631455250186219887, 83693447394047902291471577334059607393247639616279751, 329463690914221728812508410679927486798969786162893637, 1297170059750357423205123294888097042137478455106639437, 5108083609552456532412586470323794465639674111159997773, 20118209227454961184781981741413984672652876758931488259, 79248207702202821113818398278401388812603775797469402731, 312217318367757556523403042568847194679585380207042183229, 1230242115090490516542203810313306359579005945918500884279
Generating function in Maple syntax:
1/2*(-(x+1)*(x-1)^2*(1-4*x)^(1/2)+x^3-3*x^2-x+1)/x/(x^2+x-1)/(x-1)
Generating function in latex syntax:
\frac{-\left(x +1\right) \left(x -1\right)^{2} \sqrt{1-4 x}+x^{3}-3 x^{2}-x +1}{2 x \left(x^{2}+x -1\right) \left(x -1\right)}
Generating function in sympy syntax:
(x**3/2 - 3*x**2/2 - x/2 + sqrt(1 - 4*x)*(-x - 1)*(x - 1)**2/2 + 1/2)/(x*(x - 1)*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
x*(x-1)^2*(x^2+x-1)^2*F(x)^2-(x-1)*(x^2+x-1)*(x^3-3*x^2-x+1)*F(x)+x^6-2*x^5-2*x^4+6*x^3-3*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(x -1\right)^{2} \left(x^{2}+x -1\right)^{2} F \! \left(x \right)^{2}-\left(x -1\right) \left(x^{2}+x -1\right) \left(x^{3}-3 x^{2}-x +1\right) F \! \left(x \right)+x^{6}-2 x^{5}-2 x^{4}+6 x^{3}-3 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 61
a(n+5) = 2*(1+2*n)/(6+n)*a(n)+3*n/(6+n)*a(1+n)-(22+9*n)/(6+n)*a(n+2)-2*(n+5)/(6+n)*a(n+3)+(24+5*n)/(6+n)*a(n+4)+12/(6+n), 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) = 61
a \! \left(n +5\right) = \frac{2 \left(1+2 n \right) a \! \left(n \right)}{6+n}+\frac{3 n a \! \left(1+n \right)}{6+n}-\frac{\left(22+9 n \right) a \! \left(n +2\right)}{6+n}-\frac{2 \left(n +5\right) a \! \left(n +3\right)}{6+n}+\frac{\left(24+5 n \right) a \! \left(n +4\right)}{6+n}+\frac{12}{6+n}, \quad n \geq 6
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21487/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[12,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[63,x]
F[4,x] = F[12,x]*F[5,x]
F[5,x] = F[26,x]+F[6,x]
F[6,x] = F[16,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[15,x] = F[12,x]*F[8,x]
F[16,x] = F[12,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[19,x]
F[19,x] = F[20,x]+F[23,x]
F[20,x] = F[12,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = x^2
F[23,x] = F[17,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[12,x]*F[17,x]
F[26,x] = F[27,x]+F[45,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[29,x]
F[29,x] = F[12,x]*F[30,x]
F[30,x] = F[1,x]+F[28,x]
F[31,x] = F[32,x]+F[33,x]+F[35,x]
F[32,x] = 0
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[31,x]+F[8,x]
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[37,x]+F[41,x]
F[37,x] = F[28,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[12,x]+F[38,x]
F[41,x] = F[31,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[12,x]*F[44,x]
F[44,x] = F[14,x]+F[42,x]
F[45,x] = F[46,x]+F[50,x]
F[46,x] = F[32,x]+F[47,x]+F[49,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[12,x]+F[46,x]
F[49,x] = F[12,x]*F[28,x]
F[50,x] = 2*F[32,x]+F[51,x]+F[53,x]
F[51,x] = F[12,x]*F[52,x]
F[52,x] = F[17,x]+F[50,x]
F[53,x] = F[12,x]*F[54,x]
F[54,x] = F[55,x]+F[59,x]
F[55,x] = F[46,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[12,x]*F[58,x]
F[58,x] = F[21,x]+F[56,x]
F[59,x] = F[50,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[24,x]+F[60,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[65,x,1]
F[65,x,k[0]] = F[1,x]+F[107,x,k[0]]+F[109,x,k[0]]+F[66,x,k[0]]
F[66,x,k[0]] = F[12,x]*F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]+F[84,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]+F[77,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]+F[74,x,k[0]]
F[70,x,k[0]] = F[1,x]+F[71,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]
F[72,x,k[0]] = F[70,x,k[0]]*F[73,x,k[0]]
F[73,x,k[0]] = k[0]*x
F[74,x,k[0]] = F[75,x,k[0]]+F[8,x]
F[75,x,k[0]] = F[76,x,k[0]]
F[76,x,k[0]] = F[73,x,k[0]]*F[74,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]+F[81,x,k[0]]
F[78,x,k[0]] = F[12,x]+F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[73,x,k[0]]*F[78,x,k[0]]
F[81,x,k[0]] = F[17,x]+F[82,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[73,x,k[0]]*F[81,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]+F[96,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]+F[91,x,k[0]]
F[86,x,k[0]] = F[28,x]+F[87,x,k[0]]
F[87,x,k[0]] = F[32,x]+F[88,x,k[0]]+F[90,x,k[0]]
F[88,x,k[0]] = F[12,x]*F[89,x,k[0]]
F[89,x,k[0]] = F[71,x,k[0]]+F[87,x,k[0]]
F[90,x,k[0]] = F[73,x,k[0]]*F[86,x,k[0]]
F[91,x,k[0]] = F[31,x]+F[92,x,k[0]]
F[92,x,k[0]] = 2*F[32,x]+F[93,x,k[0]]+F[95,x,k[0]]
F[93,x,k[0]] = F[12,x]*F[94,x,k[0]]
F[94,x,k[0]] = F[75,x,k[0]]+F[92,x,k[0]]
F[95,x,k[0]] = F[73,x,k[0]]*F[91,x,k[0]]
F[96,x,k[0]] = F[102,x,k[0]]+F[97,x,k[0]]
F[97,x,k[0]] = F[46,x]+F[98,x,k[0]]
F[98,x,k[0]] = 2*F[32,x]+F[101,x,k[0]]+F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[12,x]
F[100,x,k[0]] = F[79,x,k[0]]+F[98,x,k[0]]
F[101,x,k[0]] = F[73,x,k[0]]*F[97,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]+F[50,x]
F[103,x,k[0]] = 3*F[32,x]+F[104,x,k[0]]+F[106,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]*F[12,x]
F[105,x,k[0]] = F[103,x,k[0]]+F[82,x,k[0]]
F[106,x,k[0]] = F[102,x,k[0]]*F[73,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]*F[12,x]
F[108,x,k[0]] = 1/(-1+k[0])*(F[65,x,k[0]]*k[0]-F[65,x,1])
F[109,x,k[0]] = F[65,x,k[0]]*F[73,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_{4}\! \left(x \right)+F_{63}\! \left(x \right)
F_{4}\! \left(x \right) = F_{12}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{26}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{16}\! \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_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
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_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = x^{2}
F_{23}\! \left(x \right) = F_{17}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{45}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = 0
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{31}\! \left(x \right)+F_{8}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{37}\! \left(x \right) = F_{28}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right)+F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = F_{31}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{14}\! \left(x \right)+F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{50}\! \left(x \right)
F_{46}\! \left(x \right) = F_{32}\! \left(x \right)+F_{47}\! \left(x \right)+F_{49}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right)+F_{46}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{50}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{51}\! \left(x \right)+F_{53}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{17}\! \left(x \right)+F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{59}\! \left(x \right)
F_{55}\! \left(x \right) = F_{46}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{21}\! \left(x \right)+F_{56}\! \left(x \right)
F_{59}\! \left(x \right) = F_{50}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{24}\! \left(x \right)+F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x , 1\right)
F_{65}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{107}\! \left(x , y\right)+F_{109}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{70}\! \left(x , y\right) F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = y x
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{73}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{12}\! \left(x \right)+F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{73}\! \left(x , y\right) F_{78}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{73}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{32}\! \left(x \right)+F_{88}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{71}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{73}\! \left(x , y\right) F_{86}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = 2 F_{32}\! \left(x \right)+F_{93}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{73}\! \left(x , y\right) F_{91}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{46}\! \left(x \right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = 2 F_{32}\! \left(x \right)+F_{101}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{100}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{73}\! \left(x , y\right) F_{97}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{50}\! \left(x \right)
F_{103}\! \left(x , y\right) = 3 F_{32}\! \left(x \right)+F_{104}\! \left(x , y\right)+F_{106}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{73}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{108}\! \left(x , y\right) = \frac{y F_{65}\! \left(x , y\right)-F_{65}\! \left(x , 1\right)}{-1+y}
F_{109}\! \left(x , y\right) = F_{65}\! \left(x , y\right) F_{73}\! \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_4(x) + F_63(x))
Eq(F_4(x), F_12(x)*F_5(x))
Eq(F_5(x), F_26(x) + F_6(x))
Eq(F_6(x), F_16(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))
Eq(F_15(x), F_12(x)*F_8(x))
Eq(F_16(x), F_12(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_12(x)*F_19(x))
Eq(F_19(x), F_20(x) + F_23(x))
Eq(F_20(x), F_12(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), x**2)
Eq(F_23(x), F_17(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_12(x)*F_17(x))
Eq(F_26(x), F_27(x) + F_45(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_12(x)*F_30(x))
Eq(F_30(x), F_1(x) + F_28(x))
Eq(F_31(x), F_32(x) + F_33(x) + F_35(x))
Eq(F_32(x), 0)
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_31(x) + F_8(x))
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_41(x))
Eq(F_37(x), F_28(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_12(x) + F_38(x))
Eq(F_41(x), F_31(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_12(x)*F_44(x))
Eq(F_44(x), F_14(x) + F_42(x))
Eq(F_45(x), F_46(x) + F_50(x))
Eq(F_46(x), F_32(x) + F_47(x) + F_49(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_12(x) + F_46(x))
Eq(F_49(x), F_12(x)*F_28(x))
Eq(F_50(x), 2*F_32(x) + F_51(x) + F_53(x))
Eq(F_51(x), F_12(x)*F_52(x))
Eq(F_52(x), F_17(x) + F_50(x))
Eq(F_53(x), F_12(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_59(x))
Eq(F_55(x), F_46(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_12(x)*F_58(x))
Eq(F_58(x), F_21(x) + F_56(x))
Eq(F_59(x), F_50(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_24(x) + F_60(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_65(x, 1))
Eq(F_65(x, k_0), F_1(x) + F_107(x, k_0) + F_109(x, k_0) + F_66(x, k_0))
Eq(F_66(x, k_0), F_12(x)*F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0) + F_84(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0) + F_77(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0) + F_74(x, k_0))
Eq(F_70(x, k_0), F_1(x) + F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0))
Eq(F_72(x, k_0), F_70(x, k_0)*F_73(x, k_0))
Eq(F_73(x, k_0), k_0*x)
Eq(F_74(x, k_0), F_75(x, k_0) + F_8(x))
Eq(F_75(x, k_0), F_76(x, k_0))
Eq(F_76(x, k_0), F_73(x, k_0)*F_74(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0) + F_81(x, k_0))
Eq(F_78(x, k_0), F_12(x) + F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_73(x, k_0)*F_78(x, k_0))
Eq(F_81(x, k_0), F_17(x) + F_82(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_73(x, k_0)*F_81(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0) + F_96(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0) + F_91(x, k_0))
Eq(F_86(x, k_0), F_28(x) + F_87(x, k_0))
Eq(F_87(x, k_0), F_32(x) + F_88(x, k_0) + F_90(x, k_0))
Eq(F_88(x, k_0), F_12(x)*F_89(x, k_0))
Eq(F_89(x, k_0), F_71(x, k_0) + F_87(x, k_0))
Eq(F_90(x, k_0), F_73(x, k_0)*F_86(x, k_0))
Eq(F_91(x, k_0), F_31(x) + F_92(x, k_0))
Eq(F_92(x, k_0), 2*F_32(x) + F_93(x, k_0) + F_95(x, k_0))
Eq(F_93(x, k_0), F_12(x)*F_94(x, k_0))
Eq(F_94(x, k_0), F_75(x, k_0) + F_92(x, k_0))
Eq(F_95(x, k_0), F_73(x, k_0)*F_91(x, k_0))
Eq(F_96(x, k_0), F_102(x, k_0) + F_97(x, k_0))
Eq(F_97(x, k_0), F_46(x) + F_98(x, k_0))
Eq(F_98(x, k_0), F_101(x, k_0) + 2*F_32(x) + F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_12(x))
Eq(F_100(x, k_0), F_79(x, k_0) + F_98(x, k_0))
Eq(F_101(x, k_0), F_73(x, k_0)*F_97(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0) + F_50(x))
Eq(F_103(x, k_0), F_104(x, k_0) + F_106(x, k_0) + 3*F_32(x))
Eq(F_104(x, k_0), F_105(x, k_0)*F_12(x))
Eq(F_105(x, k_0), F_103(x, k_0) + F_82(x, k_0))
Eq(F_106(x, k_0), F_102(x, k_0)*F_73(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0)*F_12(x))
Eq(F_108(x, k_0), (k_0*F_65(x, k_0) - F_65(x, 1))/(k_0 - 1))
Eq(F_109(x, k_0), F_65(x, k_0)*F_73(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, 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