0132_0213_1032_1230_3012
Counting sequence:
1, 1, 2, 6, 19, 51, 126, 308, 758, 1887, 4749, 12061, 30852, 79358, 204992, 531229, 1380031, 3591719, 9361130, 24424152, 63777050, 166639675, 435609313, 1139126145, 2979650064, 7795594306, 20398686916, 53383596473, 139718398003, 365704245867, 957259729014, 2505805870076, 6559619981822, 17171978669463, 44954165850357, 117686219557669, 308095895838876, 806584276683974, 2111622556019720, 5528214642037717, 14472883882824295, 37890162050351855, 99197052385925378, 259699895391128160, 679900434433043234, 1779997009325661811, 4660081796583931081, 12200230786837269513, 31940575377285982248, 83621424972603875722, 218923558797094859404, 573148969934088937841, 1500522788039661048667, 3928418268259814827443, 10284729764899239726222, 26925766522772374420484, 70492560796111996211846, 184551897850992569590479, 483163096727789525870685, 1264937320274330267226157, 3311648719979282329359540, 8670008551431957995680910, 22698376357853925910207568, 59425119369205219110582925, 155576979443913712746283279, 407305814350841795221803191, 1066340454385226521123710746, 2791715530358072474020061928, 7308806099795468418157016618, 19134702695241300929832710827, 50095301838354391890524277169, 131151202524673824115466798481, 343358305145371034759109544512, 898923711730847278659469113298, 2353412827685986943661432848212, 6161314766604746072547160459049, 16130531462683516695209692002691, 42230279602556335471664244836859, 110560307307206553633855724842150, 289450642243505454871079360456972, 757791619272194072471674307920910, 1983924215270845289751497622046215, 5193981025935878858030835921512133, 13598018861327865417892924270848565, 35600075555629865680640553795333324, 93202207800726028222958638973103446, 244006547836876812232928623536816536, 638817435690561595040991877209313093, 1672445759196122346142987880678279863, 4378519841820434190092243216189351807, 11463113766110437717863285958250160434, 30010821456201393951476094033104144496, 78569350601874774113362347171603282482, 205697230348184988343565432818064946403, 538522340440204310829443097512042247577, 1409869790967476183972542111008972606489, 3691087032452320720749499872485438824536, 9663391306369678937607910873609221433114, 25299086886617102010753219710275473299740, 66233869353402398932034122501913937869537, 173402521173431638460153376833299555562155
Generating function in Maple syntax:
(2*x^10-x^9-16*x^8+9*x^7+9*x^6+x^5+x^4-18*x^3+18*x^2-7*x+1)/(2*x-1)/(x^2-3*x+1)/(x^2+x-1)/(x-1)^2
Generating function in latex syntax:
\frac{2 x^{10}-x^{9}-16 x^{8}+9 x^{7}+9 x^{6}+x^{5}+x^{4}-18 x^{3}+18 x^{2}-7 x +1}{\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x^{2}+x -1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(2*x**10 - x**9 - 16*x**8 + 9*x**7 + 9*x**6 + x**5 + x**4 - 18*x**3 + 18*x**2 - 7*x + 1)/((x - 1)**2*(2*x - 1)*(x**2 - 3*x + 1)*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
-(2*x-1)*(x^2-3*x+1)*(x^2+x-1)*(x-1)^2*F(x)+2*x^10-x^9-16*x^8+9*x^7+9*x^6+x^5+x^4-18*x^3+18*x^2-7*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x^{2}+x -1\right) \left(x -1\right)^{2} F \! \left(x \right)+2 x^{10}-x^{9}-16 x^{8}+9 x^{7}+9 x^{6}+x^{5}+x^{4}-18 x^{3}+18 x^{2}-7 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,17/2,n = 1,6,n = 2,4,n = 3,1,0)+1/10*(5-5^(1/2))*(3/2-1/2*5^(1/2))^(-n)+1/10*(5+5^(1/2))*(3/2+1/2*5^(1/2))^(-n)-1/5*(-1/2*5^(1/2)-1/2)^(-n)*5^(1/2)+1/5*(1/2*5^(1/2)-1/2)^(-n)*5^(1/2)+n+2^(-1+n)-9
Explicit closed form in latex syntax:
\left(\left\{\begin{array}{cc}\frac{17}{2} & n =0 \\ 6 & n =1 \\ 4 & n =2 \\ 1 & n =3 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)+\frac{\left(5-\sqrt{5}\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{10}+\frac{\left(5+\sqrt{5}\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{10}-\frac{\left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n} \sqrt{5}}{5}+\frac{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n} \sqrt{5}}{5}+n +2^{-1+n}-9
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 51
a(6) = 126
a(7) = 308
a(8) = 758
a(9) = 1887
a(10) = 4749
a(n+5) = -2*a(n)+5*a(n+1)+4*a(n+2)-11*a(n+3)+6*a(n+4)-n+10, n >= 11
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) = 51
a \! \left(6\right) = 126
a \! \left(7\right) = 308
a \! \left(8\right) = 758
a \! \left(9\right) = 1887
a \! \left(10\right) = 4749
a \! \left(n +5\right) = -2 a \! \left(n \right)+5 a \! \left(n +1\right)+4 a \! \left(n +2\right)-11 a \! \left(n +3\right)+6 a \! \left(n +4\right)-n +10, \quad n \geq 11
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18343/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[24,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[21,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[4,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[14,x]*F[4,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[14,x]
F[24,x] = F[25,x]+F[45,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[1,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[28,x]*F[4,x]
F[31,x] = F[25,x]+F[32,x]
F[32,x] = F[33,x]+F[34,x]+F[44,x]
F[33,x] = 0
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[37,x]+F[4,x]
F[37,x] = F[38,x]
F[38,x] = F[29,x]*F[4,x]
F[39,x] = F[40,x]+F[42,x]
F[40,x] = F[33,x]+F[34,x]+F[41,x]
F[41,x] = F[25,x]*F[4,x]
F[42,x] = F[43,x]
F[43,x] = F[32,x]*F[4,x]
F[44,x] = F[31,x]*F[4,x]
F[45,x] = F[33,x]+F[46,x]+F[87,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[48,x]+F[55,x]
F[48,x] = F[11,x]+F[49,x]
F[49,x] = F[33,x]+F[50,x]+F[53,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[11,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[29,x]
F[55,x] = F[56,x]+F[77,x]
F[56,x] = F[33,x]+F[46,x]+F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[25,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[62,x]+F[66,x]
F[62,x] = F[11,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[11,x]
F[66,x] = F[59,x]+F[67,x]
F[67,x] = 2*F[33,x]+F[68,x]+F[75,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]+F[72,x]
F[70,x] = F[71,x]
F[71,x] = F[11,x]*F[4,x]
F[72,x] = F[73,x]
F[73,x] = 2*F[33,x]+F[68,x]+F[74,x]
F[74,x] = F[4,x]*F[59,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[59,x]
F[77,x] = F[33,x]+F[78,x]+F[83,x]+F[85,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[81,x]
F[80,x] = F[71,x]
F[81,x] = F[82,x]
F[82,x] = 2*F[33,x]+F[74,x]+F[78,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[59,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[32,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[58,x]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[33,x]+F[34,x]+F[91,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[93,x]+F[99,x]
F[93,x] = F[25,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[97,x]+F[98,x]
F[97,x] = F[4,x]
F[98,x] = F[94,x]
F[99,x] = F[90,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{24}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{21}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{14}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{45}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)+F_{44}\! \left(x \right)
F_{33}\! \left(x \right) = 0
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{42}\! \left(x \right)
F_{40}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{44}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{45}\! \left(x \right) = F_{33}\! \left(x \right)+F_{46}\! \left(x \right)+F_{87}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{55}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{33}\! \left(x \right)+F_{50}\! \left(x \right)+F_{53}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \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_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{29}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{77}\! \left(x \right)
F_{56}\! \left(x \right) = F_{33}\! \left(x \right)+F_{46}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{25}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{66}\! \left(x \right)
F_{62}\! \left(x \right) = F_{11}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{11}\! \left(x \right)
F_{66}\! \left(x \right) = F_{59}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{68}\! \left(x \right)+F_{75}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{72}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{68}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{59}\! \left(x \right)
F_{77}\! \left(x \right) = F_{33}\! \left(x \right)+F_{78}\! \left(x \right)+F_{83}\! \left(x \right)+F_{85}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = F_{71}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{74}\! \left(x \right)+F_{78}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{59}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{32}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{58}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{99}\! \left(x \right)
F_{93}\! \left(x \right) = F_{25}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)+F_{98}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right)
F_{98}\! \left(x \right) = F_{94}\! \left(x \right)
F_{99}\! \left(x \right) = F_{90}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_24(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_21(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_4(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_14(x)*F_4(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_14(x))
Eq(F_24(x), F_25(x) + F_45(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_1(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_28(x)*F_4(x))
Eq(F_31(x), F_25(x) + F_32(x))
Eq(F_32(x), F_33(x) + F_34(x) + F_44(x))
Eq(F_33(x), 0)
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_37(x) + F_4(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_29(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_42(x))
Eq(F_40(x), F_33(x) + F_34(x) + F_41(x))
Eq(F_41(x), F_25(x)*F_4(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_32(x)*F_4(x))
Eq(F_44(x), F_31(x)*F_4(x))
Eq(F_45(x), F_33(x) + F_46(x) + F_87(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_55(x))
Eq(F_48(x), F_11(x) + F_49(x))
Eq(F_49(x), F_33(x) + F_50(x) + F_53(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_11(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_29(x))
Eq(F_55(x), F_56(x) + F_77(x))
Eq(F_56(x), F_33(x) + F_46(x) + F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_25(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_66(x))
Eq(F_62(x), F_11(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_11(x))
Eq(F_66(x), F_59(x) + F_67(x))
Eq(F_67(x), 2*F_33(x) + F_68(x) + F_75(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_72(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_11(x)*F_4(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), 2*F_33(x) + F_68(x) + F_74(x))
Eq(F_74(x), F_4(x)*F_59(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_59(x))
Eq(F_77(x), F_33(x) + F_78(x) + F_83(x) + F_85(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_81(x))
Eq(F_80(x), F_71(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), 2*F_33(x) + F_74(x) + F_78(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_59(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_32(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_58(x) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_33(x) + F_34(x) + F_91(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_99(x))
Eq(F_93(x), F_25(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(x), F_97(x) + F_98(x))
Eq(F_97(x), F_4(x))
Eq(F_98(x), F_94(x))
Eq(F_99(x), F_90(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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2], "pos": [[0, 0], [0, 0], [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, 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, 0, 3, 2], "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_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"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]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "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": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[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": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", 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