0132_0213_1230_2031_2130
Counting sequence:
1, 1, 2, 6, 19, 56, 155, 408, 1037, 2574, 6291, 15226, 36635, 87858, 210369, 503464, 1205115, 2886196, 6917407, 16592516, 39831993, 95693794, 230058823, 553432694, 1332074071, 3207730598, 7727592101, 18622635732, 44891669911, 108242559896, 261048294419, 629679465744, 1519083503429, 3665191978614, 8844147067035, 21342826870642, 51508452463667, 124316986793178, 300056857864233, 724259439658240, 1748233006785747, 4220039661279676, 10186940209616551, 24591174974066972, 59363798542041585, 143307786556926154, 345957396980822287, 835178625225997550, 2016226727232617263, 4867456223733347918, 11750787437611006925, 28368327584048727468, 68486035509992633263, 165337584305969754656, 399155575353268521563, 963637477196011831080, 2326408013660599383101, 5616408471616954403934, 13559134889911422344739, 32734498115560183349098, 79027770846176540042699, 190789319253193303870338, 460604968235017749579537, 1111996373475023065982296, 2684591950667431987734699, 6481168745740287893477956, 15646906383953253698672815, 37774935397167395998362548, 91196684945183800189979817, 220168120821091167306564274, 531532557654097691678174551, 1283232498262133541370705766, 3097996078443061847811412615, 7479221703676038352711085558, 18056433582848090845578835829, 43592077063473901658403305604, 105240564097992424482208730695, 254073158035840755383065565096, 613386785722420055980181874467, 1480846540586144164139063989056, 3575079489105588144392882267573, 8631004763219004195069227066694, 20837087504386841407238690263083, 50305176749678978365255125806434, 121447434959117059847878345569251, 293200034578657102090276802086698, 707847479937918431694680465047161, 1708894946097466941028859485565872, 4125637275418796064675286210745091, 9960169303506943012266373446760396, 24045975495576444212847527442042679, 58052119520947346365147196255339084, 140150212990046151717285846309015009, 338352542406189654947685911342204314, 816855291612725432428043274194648095, 1972063113252240397553674400153749982, 4760981493358405879673778245630001247, 11494026050451451293935716253972613278, 27749033495226106471010476789279457693, 66992092842833259805041210234829650780, 161733218784751816510812281705011173727
Generating function in Maple syntax:
(x^8+2*x^7-2*x^6-3*x^5+8*x^4+5*x^3-12*x^2+6*x-1)/(2*x-1)/(x^2+x-1)/(x^2+2*x-1)/(x-1)^2
Generating function in latex syntax:
\frac{x^{8}+2 x^{7}-2 x^{6}-3 x^{5}+8 x^{4}+5 x^{3}-12 x^{2}+6 x -1}{\left(2 x -1\right) \left(x^{2}+x -1\right) \left(x^{2}+2 x -1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(x**8 + 2*x**7 - 2*x**6 - 3*x**5 + 8*x**4 + 5*x**3 - 12*x**2 + 6*x - 1)/((x - 1)**2*(2*x - 1)*(x**2 + x - 1)*(x**2 + 2*x - 1))
Implicit equation for the generating function in Maple syntax:
-(2*x-1)*(x^2+x-1)*(x^2+2*x-1)*(x-1)^2*F(x)+x^8+2*x^7-2*x^6-3*x^5+8*x^4+5*x^3-12*x^2+6*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right) \left(x^{2}+x -1\right) \left(x^{2}+2 x -1\right) \left(x -1\right)^{2} F \! \left(x \right)+x^{8}+2 x^{7}-2 x^{6}-3 x^{5}+8 x^{4}+5 x^{3}-12 x^{2}+6 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/20*(28*5^(1/2)-60)*(-1/2*5^(1/2)-1/2)^(-n)+1/20*(-28*5^(1/2)-60)*(1/2*5^(1/2)-1/2)^(-n)+1/20*(-5*2^(1/2)+10)*(-1-2^(1/2))^(-n)+1/20*(5*2^(1/2)+10)*(2^(1/2)-1)^(-n)+2*n+5/4*2^n+4)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{\left(28 \sqrt{5}-60\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{20}+\frac{\left(-28 \sqrt{5}-60\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{20}+\\\frac{\left(-5 \sqrt{2}+10\right) \left(-1-\sqrt{2}\right)^{-n}}{20}+\frac{\left(5 \sqrt{2}+10\right) \left(\sqrt{2}-1\right)^{-n}}{20}+2 n +\frac{5 \,2^{n}}{4}\\+4 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 56
a(6) = 155
a(7) = 408
a(8) = 1037
a(n+5) = 2*a(n)+5*a(n+1)-3*a(n+2)-6*a(n+3)+5*a(n+4)-4*n, 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) = 19
a \! \left(5\right) = 56
a \! \left(6\right) = 155
a \! \left(7\right) = 408
a \! \left(8\right) = 1037
a \! \left(n +5\right) = 2 a \! \left(n \right)+5 a \! \left(n +1\right)-3 a \! \left(n +2\right)-6 a \! \left(n +3\right)+5 a \! \left(n +4\right)-4 n, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18471/
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[12,x]*F[4,x]
F[4,x] = F[23,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[14,x]+F[21,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[12,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]*F[14,x]
F[21,x] = F[22,x]
F[22,x] = F[12,x]*F[13,x]
F[23,x] = F[24,x]+F[33,x]
F[24,x] = F[25,x]
F[25,x] = F[12,x]*F[26,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[1,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[12,x]*F[27,x]
F[30,x] = F[24,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[12,x]*F[30,x]
F[33,x] = F[34,x]+F[35,x]+F[88,x]
F[34,x] = 0
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[37,x]+F[58,x]
F[37,x] = F[38,x]+F[6,x]
F[38,x] = F[34,x]+F[39,x]+F[44,x]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[10,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[28,x]+F[41,x]
F[44,x] = F[12,x]*F[45,x]
F[45,x] = F[43,x]+F[46,x]
F[46,x] = F[47,x]+F[56,x]
F[47,x] = F[48,x]
F[48,x] = F[12,x]*F[49,x]
F[49,x] = F[50,x]+F[53,x]
F[50,x] = F[28,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[12,x]*F[28,x]
F[53,x] = F[47,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[12,x]*F[47,x]
F[56,x] = F[57,x]
F[57,x] = F[12,x]*F[46,x]
F[58,x] = F[33,x]+F[59,x]
F[59,x] = 2*F[34,x]+F[60,x]+F[74,x]
F[60,x] = F[12,x]*F[61,x]
F[61,x] = F[62,x]+F[71,x]
F[62,x] = F[34,x]+F[63,x]+F[72,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[65,x]+F[67,x]
F[65,x] = F[10,x]+F[66,x]
F[66,x] = F[34,x]+F[39,x]+F[42,x]
F[67,x] = F[62,x]+F[68,x]
F[68,x] = 2*F[34,x]+F[60,x]+F[69,x]
F[69,x] = F[12,x]*F[70,x]
F[70,x] = F[31,x]+F[71,x]
F[71,x] = F[69,x]
F[72,x] = F[12,x]*F[73,x]
F[73,x] = F[24,x]+F[62,x]
F[74,x] = F[12,x]*F[75,x]
F[75,x] = F[70,x]+F[76,x]
F[76,x] = F[77,x]+F[86,x]
F[77,x] = F[78,x]
F[78,x] = F[12,x]*F[79,x]
F[79,x] = F[80,x]+F[83,x]
F[80,x] = F[31,x]+F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[12,x]*F[31,x]
F[83,x] = F[77,x]+F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[12,x]*F[77,x]
F[86,x] = F[87,x]
F[87,x] = F[12,x]*F[76,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[73,x]+F[90,x]
F[90,x] = F[100,x]+F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[12,x]*F[93,x]
F[93,x] = F[94,x]+F[97,x]
F[94,x] = F[24,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[12,x]*F[24,x]
F[97,x] = F[91,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[12,x]*F[91,x]
F[100,x] = F[101,x]
F[101,x] = F[12,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{23}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
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_{12}\! \left(x \right) F_{16}\! \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_{12}\! \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_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{33}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{24}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)+F_{88}\! \left(x \right)
F_{34}\! \left(x \right) = 0
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_{58}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{6}\! \left(x \right)
F_{38}\! \left(x \right) = F_{34}\! \left(x \right)+F_{39}\! \left(x \right)+F_{44}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{10}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{28}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{56}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{53}\! \left(x \right)
F_{50}\! \left(x \right) = F_{28}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{53}\! \left(x \right) = F_{47}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{58}\! \left(x \right) = F_{33}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{60}\! \left(x \right)+F_{74}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{71}\! \left(x \right)
F_{62}\! \left(x \right) = F_{34}\! \left(x \right)+F_{63}\! \left(x \right)+F_{72}\! \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 \right)+F_{67}\! \left(x \right)
F_{65}\! \left(x \right) = F_{10}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{34}\! \left(x \right)+F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{67}\! \left(x \right) = F_{62}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{60}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{31}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{69}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{24}\! \left(x \right)+F_{62}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{70}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{86}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{83}\! \left(x \right)
F_{80}\! \left(x \right) = F_{31}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{83}\! \left(x \right) = F_{77}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{76}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{73}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{100}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{97}\! \left(x \right)
F_{94}\! \left(x \right) = F_{24}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{97}\! \left(x \right) = F_{91}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{12}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_23(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_21(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_12(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)*F_14(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_12(x)*F_13(x))
Eq(F_23(x), F_24(x) + F_33(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_12(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_1(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_12(x)*F_27(x))
Eq(F_30(x), F_24(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_12(x)*F_30(x))
Eq(F_33(x), F_34(x) + F_35(x) + F_88(x))
Eq(F_34(x), 0)
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_58(x))
Eq(F_37(x), F_38(x) + F_6(x))
Eq(F_38(x), F_34(x) + F_39(x) + F_44(x))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_10(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_28(x) + F_41(x))
Eq(F_44(x), F_12(x)*F_45(x))
Eq(F_45(x), F_43(x) + F_46(x))
Eq(F_46(x), F_47(x) + F_56(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_12(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_53(x))
Eq(F_50(x), F_28(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_12(x)*F_28(x))
Eq(F_53(x), F_47(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_12(x)*F_47(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_12(x)*F_46(x))
Eq(F_58(x), F_33(x) + F_59(x))
Eq(F_59(x), 2*F_34(x) + F_60(x) + F_74(x))
Eq(F_60(x), F_12(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_71(x))
Eq(F_62(x), F_34(x) + F_63(x) + F_72(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_67(x))
Eq(F_65(x), F_10(x) + F_66(x))
Eq(F_66(x), F_34(x) + F_39(x) + F_42(x))
Eq(F_67(x), F_62(x) + F_68(x))
Eq(F_68(x), 2*F_34(x) + F_60(x) + F_69(x))
Eq(F_69(x), F_12(x)*F_70(x))
Eq(F_70(x), F_31(x) + F_71(x))
Eq(F_71(x), F_69(x))
Eq(F_72(x), F_12(x)*F_73(x))
Eq(F_73(x), F_24(x) + F_62(x))
Eq(F_74(x), F_12(x)*F_75(x))
Eq(F_75(x), F_70(x) + F_76(x))
Eq(F_76(x), F_77(x) + F_86(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_12(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_83(x))
Eq(F_80(x), F_31(x) + F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_12(x)*F_31(x))
Eq(F_83(x), F_77(x) + F_84(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_12(x)*F_77(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_12(x)*F_76(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_73(x) + F_90(x))
Eq(F_90(x), F_100(x) + F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_12(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_97(x))
Eq(F_94(x), F_24(x) + F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_12(x)*F_24(x))
Eq(F_97(x), F_91(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_12(x)*F_91(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_12(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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0], "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, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 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, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 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}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], 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0, 2], "pos": [[0, 0], [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": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"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], "pos": 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[0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[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": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [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]]}], "requirements": 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