0123_0132_1203_1230_3012
Counting sequence:
1, 1, 2, 6, 19, 58, 173, 521, 1620, 5235, 17508, 60129, 210543, 747698, 2683619, 9712579, 35392242, 129712689, 477772814, 1767529191, 6564649533, 24467321560, 91484668085, 343063816786, 1289912546534, 4861963191293, 18367386641508, 69533618042391, 263748085988535, 1002242485110546, 3814987038990591, 14544637113000167, 55534067024567774, 212336134707251293, 812944050739711698, 3116285512087222771, 11959798420220250729, 45950804393341285108, 176733862924445728649, 680425372004853789546, 2622127042826248014058, 10113918592737409863025, 39044429914103467326680, 150853479209483398295171, 583300119601792786245955, 2257117854094840259447086, 8740328711568357762298291, 33868773757261415630785472, 131327898242310102966541760, 509552245179898613031531055, 1978261657756723603577426018, 7684785670515442285137908629, 29869166945774877749956373433, 116157871455786937850181509148, 451959718027962478646864566613, 1759414616608836885390989698956, 6852456927844909526346677795514, 26700952856774923961839259235553, 104088460289122448148686395092164, 405944995127577273961019595533923, 1583850964596120619147525082949959, 6182127958584856803408585454585106, 24139737743045629131554467760525047, 94295850558771984399621403374363631, 368479169875816668702381079568958070, 1440418573150919687319233967954093941, 5632681584560312771887403853268968986, 22033725021956517537145528908895922827, 86218923998960285873759593253378335745, 337485502510215975851931698634412314988, 1321422108420282271080237987548936113137, 5175569924646105560599531814712477991338, 20276890389709399865290181809689464661266, 79463489365077377845930604115218915186553, 311496878311103321146981024484548425605184, 1221395654430378811847650187939440712861179, 4790408930363303911366165140257821624016987, 18793142726809884575286919142813459518022374, 73745243611532458459841267582099157887600219, 289450081175264899454586077484394424559571196, 1136359577947336271932237339914474771256548528, 4462290049988320482464450223325747812676024575, 17526585015616776834737558369554884894747395610, 68854441132780194707892887737947105659685868341, 270557451039395118028652134695725483454070859265, 1063353702922273835973056000856590292789900728036, 4180080073556524734514734513797135126562344035421, 16435314834665426797069222332015341479634773816012, 64633260585762914370496792228651092135215899983330, 254224158304000796523953750263851468431616099249193, 1000134600800354781929399869506561507052598542068012, 3935312233584004685417854810703388795154306581820603, 15487357822491889407128329439658421802774480928878111, 60960876535340415751462568532589806033490828506854538, 239993345518077005168915786526997037289323026684272799, 944973797977428207852605890261980225403315156624075084, 3721443204405954385563870580993327916841675494153991332, 14657929356129575437016877925885195275977292544447170179, 57743358069601357782187700766499181362549406811848123854, 227508830794229349661819540712601504013099032975720612961, 896519947090131496687170070707925932534952222287101433133
Generating function in Maple syntax:
1/2*(-2*(x-1)^5*(x-1/2)*(1-4*x)^(1/2)-2*x^7+4*x^6-15*x^5+27*x^4-30*x^3+20*x^2-7*x+1)/x/(2*x-1)/(x-1)^5
Generating function in latex syntax:
\frac{-2 \left(x -1\right)^{5} \left(x -\frac{1}{2}\right) \sqrt{1-4 x}-2 x^{7}+4 x^{6}-15 x^{5}+27 x^{4}-30 x^{3}+20 x^{2}-7 x +1}{2 x \left(2 x -1\right) \left(x -1\right)^{5}}
Generating function in sympy syntax:
(-x**7 + 2*x**6 - 15*x**5/2 + 27*x**4/2 - 15*x**3 + 10*x**2 - 7*x/2 - sqrt(1 - 4*x)*(x - 1)**5*(x - 1/2) + 1/2)/(x*(x - 1)**5*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*(x-1)^10*F(x)^2+(2*x-1)*(2*x^7-4*x^6+15*x^5-27*x^4+30*x^3-20*x^2+7*x-1)*(x-1)^5*F(x)+x^13-26*x^11+175*x^10-585*x^9+1250*x^8-1855*x^7+1980*x^6-1537*x^5+861*x^4-339*x^3+89*x^2-14*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} \left(x -1\right)^{10} F \! \left(x \right)^{2}+\left(2 x -1\right) \left(2 x^{7}-4 x^{6}+15 x^{5}-27 x^{4}+30 x^{3}-20 x^{2}+7 x -1\right) \left(x -1\right)^{5} F \! \left(x \right)+x^{13}-26 x^{11}+175 x^{10}-585 x^{9}+1250 x^{8}-1855 x^{7}+1980 x^{6}-1537 x^{5}+861 x^{4}-339 x^{3}+89 x^{2}-14 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 58
a(6) = 173
a(7) = 521
a(8) = 1620
a(9) = 5235
a(n+3) = 8*(2*n+1)/(n+4)*a(n)-4*(5*n+8)/(n+4)*a(n+1)+2*(4*n+11)/(n+4)*a(n+2)-1/24*n*(3*n^4-52*n^3+213*n^2-176*n+132)/(n+4), n >= 10
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) = 58
a \! \left(6\right) = 173
a \! \left(7\right) = 521
a \! \left(8\right) = 1620
a \! \left(9\right) = 5235
a \! \left(n +3\right) = \frac{8 \left(2 n +1\right) a \! \left(n \right)}{n +4}-\frac{4 \left(5 n +8\right) a \! \left(n +1\right)}{n +4}+\frac{2 \left(4 n +11\right) a \! \left(n +2\right)}{n +4}-\frac{n \left(3 n^{4}-52 n^{3}+213 n^{2}-176 n +132\right)}{24 \left(n +4\right)}, \quad n \geq 10
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21512/
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[4,x]+F[41,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[24,x,k[0]]
F[14,x] = F[15,x]+F[18,x]
F[15,x] = F[1,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[11,x]*F[15,x]
F[18,x] = F[16,x]+F[19,x]
F[19,x] = F[20,x]+F[21,x]+F[23,x]
F[20,x] = 0
F[21,x] = F[11,x]*F[22,x]
F[22,x] = F[16,x]+F[19,x]
F[23,x] = F[11,x]*F[18,x]
F[24,x,k[0]] = F[25,x,k[0]]+F[33,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]+F[29,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]*F[8,x,k[0]]
F[28,x,k[0]] = F[1,x]+F[26,x,k[0]]
F[29,x,k[0]] = F[20,x]+F[30,x,k[0]]+F[32,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]*F[8,x,k[0]]
F[31,x,k[0]] = F[16,x]+F[29,x,k[0]]
F[32,x,k[0]] = F[11,x]*F[25,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]+F[37,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[11,x]*F[36,x,k[0]]
F[36,x,k[0]] = F[26,x,k[0]]+F[34,x,k[0]]
F[37,x,k[0]] = 2*F[20,x]+F[38,x,k[0]]+F[40,x,k[0]]
F[38,x,k[0]] = F[11,x]*F[39,x,k[0]]
F[39,x,k[0]] = F[29,x,k[0]]+F[37,x,k[0]]
F[40,x,k[0]] = F[11,x]*F[33,x,k[0]]
F[41,x] = F[11,x]*F[42,x]
F[42,x] = F[43,x]+F[70,x]
F[43,x] = F[44,x]+F[56,x]
F[44,x] = F[1,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[11,x]*F[47,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = F[1,x]+F[11,x]
F[49,x] = F[45,x]+F[50,x]
F[50,x] = F[20,x]+F[51,x]+F[55,x]
F[51,x] = F[11,x]*F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = F[11,x]
F[54,x] = F[50,x]
F[55,x] = F[11,x]*F[45,x]
F[56,x] = F[16,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[11,x]*F[59,x]
F[59,x] = F[60,x]+F[63,x]
F[60,x] = F[16,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[11,x]*F[16,x]
F[63,x] = F[57,x]+F[64,x]
F[64,x] = 2*F[20,x]+F[65,x]+F[69,x]
F[65,x] = F[11,x]*F[66,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[61,x]
F[68,x] = F[64,x]
F[69,x] = F[11,x]*F[57,x]
F[70,x] = F[71,x]+F[91,x]
F[71,x] = F[16,x]+F[72,x]
F[72,x] = F[20,x]+F[73,x]+F[75,x]
F[73,x] = F[11,x]*F[74,x]
F[74,x] = F[45,x]+F[72,x]
F[75,x] = F[11,x]*F[76,x]
F[76,x] = F[77,x]+F[81,x]
F[77,x] = F[16,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[11,x]*F[80,x]
F[80,x] = F[11,x]+F[78,x]
F[81,x] = F[82,x]+F[83,x]
F[82,x] = F[20,x]+F[21,x]+F[75,x]
F[83,x] = 2*F[20,x]+F[84,x]+F[87,x]
F[84,x] = F[11,x]*F[85,x]
F[85,x] = F[61,x]+F[86,x]
F[86,x] = F[84,x]
F[87,x] = F[11,x]*F[88,x]
F[88,x] = F[89,x]+F[90,x]
F[89,x] = F[78,x]
F[90,x] = F[83,x]
F[91,x] = F[92,x]+F[98,x]
F[92,x] = F[20,x]+F[93,x]+F[95,x]
F[93,x] = F[11,x]*F[94,x]
F[94,x] = F[16,x]+F[92,x]
F[95,x] = F[11,x]*F[96,x]
F[96,x] = F[16,x]+F[97,x]
F[97,x] = F[95,x]
F[98,x] = 2*F[20,x]+F[101,x]+F[99,x]
F[99,x] = F[100,x]*F[11,x]
F[100,x] = F[57,x]+F[98,x]
F[101,x] = F[102,x]*F[11,x]
F[102,x] = F[103,x]+F[104,x]
F[103,x] = F[97,x]
F[104,x] = F[101,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_{4}\! \left(x \right)+F_{41}\! \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_{24}\! \left(x , y\right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)
F_{15}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{18}\! \left(x \right) = F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{23}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{26}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{20}\! \left(x \right)+F_{30}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{16}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{25}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = 2 F_{20}\! \left(x \right)+F_{38}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{41}\! \left(x \right) = F_{11}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{70}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{56}\! \left(x \right)
F_{44}\! \left(x \right) = F_{1}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \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_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{49}\! \left(x \right) = F_{45}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{20}\! \left(x \right)+F_{51}\! \left(x \right)+F_{55}\! \left(x \right)
F_{51}\! \left(x \right) = F_{11}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right)
F_{54}\! \left(x \right) = F_{50}\! \left(x \right)
F_{55}\! \left(x \right) = F_{11}\! \left(x \right) F_{45}\! \left(x \right)
F_{56}\! \left(x \right) = F_{16}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{11}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{63}\! \left(x \right)
F_{60}\! \left(x \right) = F_{16}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right)
F_{63}\! \left(x \right) = F_{57}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{65}\! \left(x \right)+F_{69}\! \left(x \right)
F_{65}\! \left(x \right) = F_{11}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{61}\! \left(x \right)
F_{68}\! \left(x \right) = F_{64}\! \left(x \right)
F_{69}\! \left(x \right) = F_{11}\! \left(x \right) F_{57}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{91}\! \left(x \right)
F_{71}\! \left(x \right) = F_{16}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{20}\! \left(x \right)+F_{73}\! \left(x \right)+F_{75}\! \left(x \right)
F_{73}\! \left(x \right) = F_{11}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{45}\! \left(x \right)+F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{11}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{81}\! \left(x \right)
F_{77}\! \left(x \right) = F_{16}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{11}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{11}\! \left(x \right)+F_{78}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{83}\! \left(x \right)
F_{82}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{75}\! \left(x \right)
F_{83}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{84}\! \left(x \right)+F_{87}\! \left(x \right)
F_{84}\! \left(x \right) = F_{11}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{61}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{84}\! \left(x \right)
F_{87}\! \left(x \right) = F_{11}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{78}\! \left(x \right)
F_{90}\! \left(x \right) = F_{83}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{98}\! \left(x \right)
F_{92}\! \left(x \right) = F_{20}\! \left(x \right)+F_{93}\! \left(x \right)+F_{95}\! \left(x \right)
F_{93}\! \left(x \right) = F_{11}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{16}\! \left(x \right)+F_{92}\! \left(x \right)
F_{95}\! \left(x \right) = F_{11}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{16}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{95}\! \left(x \right)
F_{98}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{101}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{11}\! \left(x \right)
F_{100}\! \left(x \right) = F_{57}\! \left(x \right)+F_{98}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{11}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{104}\! \left(x \right)
F_{103}\! \left(x \right) = F_{97}\! \left(x \right)
F_{104}\! \left(x \right) = F_{101}\! \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_4(x) + F_41(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_24(x, k_0))
Eq(F_14(x), F_15(x) + F_18(x))
Eq(F_15(x), F_1(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_11(x)*F_15(x))
Eq(F_18(x), F_16(x) + F_19(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_23(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_11(x)*F_22(x))
Eq(F_22(x), F_16(x) + F_19(x))
Eq(F_23(x), F_11(x)*F_18(x))
Eq(F_24(x, k_0), F_25(x, k_0) + F_33(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0) + F_29(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0)*F_8(x, k_0))
Eq(F_28(x, k_0), F_1(x) + F_26(x, k_0))
Eq(F_29(x, k_0), F_20(x) + F_30(x, k_0) + F_32(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0)*F_8(x, k_0))
Eq(F_31(x, k_0), F_16(x) + F_29(x, k_0))
Eq(F_32(x, k_0), F_11(x)*F_25(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0) + F_37(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_11(x)*F_36(x, k_0))
Eq(F_36(x, k_0), F_26(x, k_0) + F_34(x, k_0))
Eq(F_37(x, k_0), 2*F_20(x) + F_38(x, k_0) + F_40(x, k_0))
Eq(F_38(x, k_0), F_11(x)*F_39(x, k_0))
Eq(F_39(x, k_0), F_29(x, k_0) + F_37(x, k_0))
Eq(F_40(x, k_0), F_11(x)*F_33(x, k_0))
Eq(F_41(x), F_11(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_70(x))
Eq(F_43(x), F_44(x) + F_56(x))
Eq(F_44(x), F_1(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_11(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_49(x))
Eq(F_48(x), F_1(x) + F_11(x))
Eq(F_49(x), F_45(x) + F_50(x))
Eq(F_50(x), F_20(x) + F_51(x) + F_55(x))
Eq(F_51(x), F_11(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), F_11(x))
Eq(F_54(x), F_50(x))
Eq(F_55(x), F_11(x)*F_45(x))
Eq(F_56(x), F_16(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_11(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_63(x))
Eq(F_60(x), F_16(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_11(x)*F_16(x))
Eq(F_63(x), F_57(x) + F_64(x))
Eq(F_64(x), 2*F_20(x) + F_65(x) + F_69(x))
Eq(F_65(x), F_11(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_61(x))
Eq(F_68(x), F_64(x))
Eq(F_69(x), F_11(x)*F_57(x))
Eq(F_70(x), F_71(x) + F_91(x))
Eq(F_71(x), F_16(x) + F_72(x))
Eq(F_72(x), F_20(x) + F_73(x) + F_75(x))
Eq(F_73(x), F_11(x)*F_74(x))
Eq(F_74(x), F_45(x) + F_72(x))
Eq(F_75(x), F_11(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_81(x))
Eq(F_77(x), F_16(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_11(x)*F_80(x))
Eq(F_80(x), F_11(x) + F_78(x))
Eq(F_81(x), F_82(x) + F_83(x))
Eq(F_82(x), F_20(x) + F_21(x) + F_75(x))
Eq(F_83(x), 2*F_20(x) + F_84(x) + F_87(x))
Eq(F_84(x), F_11(x)*F_85(x))
Eq(F_85(x), F_61(x) + F_86(x))
Eq(F_86(x), F_84(x))
Eq(F_87(x), F_11(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_90(x))
Eq(F_89(x), F_78(x))
Eq(F_90(x), F_83(x))
Eq(F_91(x), F_92(x) + F_98(x))
Eq(F_92(x), F_20(x) + F_93(x) + F_95(x))
Eq(F_93(x), F_11(x)*F_94(x))
Eq(F_94(x), F_16(x) + F_92(x))
Eq(F_95(x), F_11(x)*F_96(x))
Eq(F_96(x), F_16(x) + F_97(x))
Eq(F_97(x), F_95(x))
Eq(F_98(x), F_101(x) + 2*F_20(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_11(x))
Eq(F_100(x), F_57(x) + F_98(x))
Eq(F_101(x), F_102(x)*F_11(x))
Eq(F_102(x), F_103(x) + F_104(x))
Eq(F_103(x), F_97(x))
Eq(F_104(x), F_101(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:
{"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": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "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": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "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": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"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": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"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], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": 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