0231_0312_1203_3012
Counting sequence:
1, 1, 2, 6, 20, 65, 205, 641, 2024, 6521, 21512, 72599, 249920, 874613, 3101878, 11120360, 40219378, 146526775, 537111827, 1979229556, 7326789376, 27232101125, 101579795059, 380132134180, 1426693435046, 5368871670655, 20253248623191, 76573985368690, 290113908764868, 1101262863040753, 4187840921891385, 15951951102664393, 60857605243391936, 232514922820931545, 889576273539770432, 3407821737493883083, 13070730112823380264, 50190648853219771405, 192938474617563800330, 742443078114806810925, 2859781920296515363232, 11025720080818245647093, 42546683548388650911172, 164320209760530251671337, 635134708901723614790544, 2456826828010811779267125, 9510478363242680862622104, 36841350033979706240172059, 142810844253721835165465236, 553945747071914150594342129, 2150019161504966136552658122, 8349795039997130021600452587, 32445737125850036072088443472, 126147415211037367142003740805, 490714641432927845681305254250, 1909858479303745215668934872147, 7436813468057147997075482800188, 28972005887934151525086827559825, 112919528391671686177234206384546, 440302923343831142166625940228087, 1717590603748911785824147093962616, 6702968631347176338048076268611181, 26169072710918361891775115965183062, 102206271925507922861981141238158256, 399327795388257276231804207569382666, 1560771309585129395883088981532892623, 6102417767309573930445883022742767563, 23867830013524364988123481097044657508, 93383013789221679115383670402152428952, 365479135928349036429026074549952306733, 1430846454996027962094180432379819728627, 5603448299309290813990992931955858434736, 21950575900700239526235201662994704719414, 86012416815677144856565903865730026356319, 337130215819321510202783627682393782519907, 1321758927133390761013706721480972057452910, 5183483866801694023287989675364186701699772, 20333080340642158702908416930874207215201561, 79779929141083344168531886956848601503454853, 313105277238554871645894739152651270679852310, 1229109944648587184755283270608314058233401246, 4826053286015689407023183413682404571633717879, 18953614978001556175499874184051404909618838505, 74454023573187283807986205165744823676688863896, 292535225548744950590986161272860445327492653496, 1149634601785614691254840161730763622226563687213, 4518882055579940777589665721374046750117125972503, 17765999362736469082672614936505857495979334717858, 69860829833854341568660232113919887445978567589202, 274764975941812307269816062209241743002767288117563, 1080863068323705381585383501043136397122160430790797, 4252652088726714907171446092351797490967086412317696, 16735055633767783636341095908697327249675403441752044, 65867459133623680859773639390350440551387514530024009, 259292212492546557685937267875679121457022520900312727, 1020895452256364313031024168969298799549437282552708520, 4020173232131180421853983169038858309686435361896675682, 15833556855388078014433120362095710116030376664757061251, 62370752960347878181725390513850787474736675255016678403, 245725867844560092891999629623748223274888199628494584030, 968248440120555170648581657261534649690607663620037921536
Generating function in Maple syntax:
-1/2*(-1+(1-4*x)^(1/2))/x*(2*x^4-6*x^3+9*x^2-5*x+1)/(2*x-1)/(x-1)^3
Generating function in latex syntax:
-\frac{\left(-1+\sqrt{1-4 x}\right) \left(2 x^{4}-6 x^{3}+9 x^{2}-5 x +1\right)}{2 x \left(2 x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(1/2 - sqrt(1 - 4*x)/2)*(2*x**4 - 6*x**3 + 9*x**2 - 5*x + 1)/(x*(x - 1)**3*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*(x-1)^6*F(x)^2-(2*x-1)*(2*x^4-6*x^3+9*x^2-5*x+1)*(x-1)^3*F(x)+(2*x^4-6*x^3+9*x^2-5*x+1)^2 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} \left(x -1\right)^{6} F \! \left(x \right)^{2}-\left(2 x -1\right) \left(2 x^{4}-6 x^{3}+9 x^{2}-5 x +1\right) \left(x -1\right)^{3} F \! \left(x \right)+\left(2 x^{4}-6 x^{3}+9 x^{2}-5 x +1\right)^{2} = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 65
a(6) = 205
a(7) = 641
a(8) = 2024
a(n+7) = 8*(1+2*n)/(n+8)*a(n)-4*(27+19*n)/(n+8)*a(n+1)+2*(224+85*n)/(n+8)*a(n+2)-70*(11+3*n)/(n+8)*a(n+3)+49*(14+3*n)/(n+8)*a(n+4)-2*(166+29*n)/(n+8)*a(n+5)+2*(41+6*n)/(n+8)*a(n+6)+(n+2)/(n+8), n >= 9
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) = 65
a \! \left(6\right) = 205
a \! \left(7\right) = 641
a \! \left(8\right) = 2024
a \! \left(n +7\right) = \frac{8 \left(1+2 n \right) a \! \left(n \right)}{n +8}-\frac{4 \left(27+19 n \right) a \! \left(n +1\right)}{n +8}+\frac{2 \left(224+85 n \right) a \! \left(n +2\right)}{n +8}-\frac{70 \left(11+3 n \right) a \! \left(n +3\right)}{n +8}+\frac{49 \left(14+3 n \right) a \! \left(n +4\right)}{n +8}-\frac{2 \left(166+29 n \right) a \! \left(n +5\right)}{n +8}+\frac{2 \left(41+6 n \right) a \! \left(n +6\right)}{n +8}+\frac{n +2}{n +8}, \quad n \geq 9
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21409/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[19,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[92,x]
F[4,x] = F[19,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[7,x,k[0]]+F[89,x,k[0]]+F[91,x,k[0]]
F[7,x,k[0]] = F[19,x]*F[8,x,k[0]]
F[8,x,k[0]] = F[44,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]+F[22,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[15,x,k[0]]
F[11,x,k[0]] = F[1,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[11,x,k[0]]*F[14,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[15,x,k[0]] = F[16,x]+F[20,x,k[0]]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[19,x]
F[18,x] = F[1,x]+F[16,x]
F[19,x] = x
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[14,x,k[0]]*F[15,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]+F[32,x,k[0]]
F[23,x,k[0]] = F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[19,x]*F[26,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[1,x]+F[24,x]
F[28,x] = F[16,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[19,x]*F[31,x]
F[31,x] = F[24,x]+F[29,x]
F[32,x,k[0]] = F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[19,x]*F[35,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[16,x]+F[33,x]
F[37,x] = F[38,x]+F[41,x]
F[38,x] = F[39,x]
F[39,x] = F[19,x]*F[40,x]
F[40,x] = F[16,x]+F[38,x]
F[41,x] = F[42,x]
F[42,x] = F[19,x]*F[43,x]
F[43,x] = F[33,x]+F[41,x]
F[44,x,k[0]] = F[45,x,k[0]]+F[62,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]+F[52,x,k[0]]
F[46,x,k[0]] = F[16,x]+F[47,x,k[0]]
F[47,x,k[0]] = F[48,x]+F[49,x,k[0]]+F[51,x,k[0]]
F[48,x] = 0
F[49,x,k[0]] = F[19,x]*F[50,x,k[0]]
F[50,x,k[0]] = F[12,x,k[0]]+F[47,x,k[0]]
F[51,x,k[0]] = F[14,x,k[0]]*F[46,x,k[0]]
F[52,x,k[0]] = F[53,x]+F[58,x,k[0]]
F[53,x] = F[48,x]+F[54,x]+F[56,x]
F[54,x] = F[19,x]*F[55,x]
F[55,x] = F[16,x]+F[53,x]
F[56,x] = F[19,x]*F[57,x]
F[57,x] = F[16,x]+F[53,x]
F[58,x,k[0]] = 2*F[48,x]+F[59,x,k[0]]+F[61,x,k[0]]
F[59,x,k[0]] = F[19,x]*F[60,x,k[0]]
F[60,x,k[0]] = F[20,x,k[0]]+F[58,x,k[0]]
F[61,x,k[0]] = F[14,x,k[0]]*F[52,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]+F[76,x,k[0]]
F[63,x,k[0]] = F[64,x]
F[64,x] = F[48,x]+F[65,x]+F[67,x]
F[65,x] = F[19,x]*F[66,x]
F[66,x] = F[24,x]+F[64,x]
F[67,x] = F[19,x]*F[68,x]
F[68,x] = F[28,x]+F[69,x]
F[69,x] = F[70,x]+F[73,x]
F[70,x] = F[71,x]
F[71,x] = F[19,x]*F[72,x]
F[72,x] = F[16,x]+F[70,x]
F[73,x] = F[74,x]
F[74,x] = F[19,x]*F[75,x]
F[75,x] = F[29,x]+F[73,x]
F[76,x,k[0]] = F[77,x]
F[77,x] = 2*F[48,x]+F[78,x]+F[80,x]
F[78,x] = F[19,x]*F[79,x]
F[79,x] = F[33,x]+F[77,x]
F[80,x] = F[19,x]*F[81,x]
F[81,x] = F[37,x]+F[82,x]
F[82,x] = F[83,x]+F[86,x]
F[83,x] = F[84,x]
F[84,x] = F[19,x]*F[85,x]
F[85,x] = F[38,x]+F[83,x]
F[86,x] = F[87,x]
F[87,x] = F[19,x]*F[88,x]
F[88,x] = F[41,x]+F[86,x]
F[89,x,k[0]] = F[19,x]*F[90,x,k[0]]
F[90,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[91,x,k[0]] = F[14,x,k[0]]*F[6,x,k[0]]
F[92,x] = F[19,x]*F[93,x]
F[93,x] = F[94,x]+F[96,x]
F[94,x] = F[18,x]+F[95,x]
F[95,x] = F[24,x]+F[33,x]
F[96,x] = F[57,x]+F[97,x]
F[97,x] = F[64,x]+F[77,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_{19}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{92}\! \left(x \right)
F_{4}\! \left(x \right) = F_{19}\! \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_{7}\! \left(x , y\right)+F_{89}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = y x
F_{15}\! \left(x , y\right) = F_{16}\! \left(x \right)+F_{20}\! \left(x , y\right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{19}\! \left(x \right) = x
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{15}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{19}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{28}\! \left(x \right) = F_{16}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{19}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{24}\! \left(x \right)+F_{29}\! \left(x \right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{19}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{16}\! \left(x \right)+F_{33}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{19}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \left(x \right)+F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{19}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{33}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{16}\! \left(x \right)+F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x \right)+F_{49}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{48}\! \left(x \right) = 0
F_{49}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{46}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x \right)+F_{58}\! \left(x , y\right)
F_{53}\! \left(x \right) = F_{48}\! \left(x \right)+F_{54}\! \left(x \right)+F_{56}\! \left(x \right)
F_{54}\! \left(x \right) = F_{19}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{16}\! \left(x \right)+F_{53}\! \left(x \right)
F_{56}\! \left(x \right) = F_{19}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{16}\! \left(x \right)+F_{53}\! \left(x \right)
F_{58}\! \left(x , y\right) = 2 F_{48}\! \left(x \right)+F_{59}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{48}\! \left(x \right)+F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{65}\! \left(x \right) = F_{19}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{24}\! \left(x \right)+F_{64}\! \left(x \right)
F_{67}\! \left(x \right) = F_{19}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{28}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{73}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{19}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{16}\! \left(x \right)+F_{70}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{19}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{29}\! \left(x \right)+F_{73}\! \left(x \right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = 2 F_{48}\! \left(x \right)+F_{78}\! \left(x \right)+F_{80}\! \left(x \right)
F_{78}\! \left(x \right) = F_{19}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{33}\! \left(x \right)+F_{77}\! \left(x \right)
F_{80}\! \left(x \right) = F_{19}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{37}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{86}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{19}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{38}\! \left(x \right)+F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{19}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{41}\! \left(x \right)+F_{86}\! \left(x \right)
F_{89}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = \frac{F_{6}\! \left(x , y\right) y -F_{6}\! \left(x , 1\right)}{-1+y}
F_{91}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{6}\! \left(x , y\right)
F_{92}\! \left(x \right) = F_{19}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{96}\! \left(x \right)
F_{94}\! \left(x \right) = F_{18}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{24}\! \left(x \right)+F_{33}\! \left(x \right)
F_{96}\! \left(x \right) = F_{57}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{64}\! \left(x \right)+F_{77}\! \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_19(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_92(x))
Eq(F_4(x), F_19(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_7(x, k_0) + F_89(x, k_0) + F_91(x, k_0))
Eq(F_7(x, k_0), F_19(x)*F_8(x, k_0))
Eq(F_8(x, k_0), F_44(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0) + F_22(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_15(x, k_0))
Eq(F_11(x, k_0), F_1(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_11(x, k_0)*F_14(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x, k_0), F_16(x) + F_20(x, k_0))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_19(x))
Eq(F_18(x), F_1(x) + F_16(x))
Eq(F_19(x), x)
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_14(x, k_0)*F_15(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0) + F_32(x, k_0))
Eq(F_23(x, k_0), F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_19(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_1(x) + F_24(x))
Eq(F_28(x), F_16(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_19(x)*F_31(x))
Eq(F_31(x), F_24(x) + F_29(x))
Eq(F_32(x, k_0), F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_19(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_16(x) + F_33(x))
Eq(F_37(x), F_38(x) + F_41(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_19(x)*F_40(x))
Eq(F_40(x), F_16(x) + F_38(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_19(x)*F_43(x))
Eq(F_43(x), F_33(x) + F_41(x))
Eq(F_44(x, k_0), F_45(x, k_0) + F_62(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0) + F_52(x, k_0))
Eq(F_46(x, k_0), F_16(x) + F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x) + F_49(x, k_0) + F_51(x, k_0))
Eq(F_48(x), 0)
Eq(F_49(x, k_0), F_19(x)*F_50(x, k_0))
Eq(F_50(x, k_0), F_12(x, k_0) + F_47(x, k_0))
Eq(F_51(x, k_0), F_14(x, k_0)*F_46(x, k_0))
Eq(F_52(x, k_0), F_53(x) + F_58(x, k_0))
Eq(F_53(x), F_48(x) + F_54(x) + F_56(x))
Eq(F_54(x), F_19(x)*F_55(x))
Eq(F_55(x), F_16(x) + F_53(x))
Eq(F_56(x), F_19(x)*F_57(x))
Eq(F_57(x), F_16(x) + F_53(x))
Eq(F_58(x, k_0), 2*F_48(x) + F_59(x, k_0) + F_61(x, k_0))
Eq(F_59(x, k_0), F_19(x)*F_60(x, k_0))
Eq(F_60(x, k_0), F_20(x, k_0) + F_58(x, k_0))
Eq(F_61(x, k_0), F_14(x, k_0)*F_52(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0) + F_76(x, k_0))
Eq(F_63(x, k_0), F_64(x))
Eq(F_64(x), F_48(x) + F_65(x) + F_67(x))
Eq(F_65(x), F_19(x)*F_66(x))
Eq(F_66(x), F_24(x) + F_64(x))
Eq(F_67(x), F_19(x)*F_68(x))
Eq(F_68(x), F_28(x) + F_69(x))
Eq(F_69(x), F_70(x) + F_73(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_19(x)*F_72(x))
Eq(F_72(x), F_16(x) + F_70(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_19(x)*F_75(x))
Eq(F_75(x), F_29(x) + F_73(x))
Eq(F_76(x, k_0), F_77(x))
Eq(F_77(x), 2*F_48(x) + F_78(x) + F_80(x))
Eq(F_78(x), F_19(x)*F_79(x))
Eq(F_79(x), F_33(x) + F_77(x))
Eq(F_80(x), F_19(x)*F_81(x))
Eq(F_81(x), F_37(x) + F_82(x))
Eq(F_82(x), F_83(x) + F_86(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_19(x)*F_85(x))
Eq(F_85(x), F_38(x) + F_83(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_19(x)*F_88(x))
Eq(F_88(x), F_41(x) + F_86(x))
Eq(F_89(x, k_0), F_19(x)*F_90(x, k_0))
Eq(F_90(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_91(x, k_0), F_14(x, k_0)*F_6(x, k_0))
Eq(F_92(x), F_19(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_96(x))
Eq(F_94(x), F_18(x) + F_95(x))
Eq(F_95(x), F_24(x) + F_33(x))
Eq(F_96(x), F_57(x) + F_97(x))
Eq(F_97(x), F_64(x) + F_77(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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 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": [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], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 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": [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], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 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, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 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], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 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": [[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], [0, 0], [3, 0]]}, {"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]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 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": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 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], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 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, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 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]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, 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