0123_0132_0231_1032_3021
Counting sequence:
1, 1, 2, 6, 19, 57, 162, 447, 1212, 3251, 8660, 22961, 60680, 159985, 421078, 1106845, 2906638, 7627419, 20004306, 52442859, 137438976, 360103463, 943330184, 2470804613, 6470918684, 16945621477, 44373285802, 116188916017, 304222822402, 796538271471, 2085509432550, 5460224907231, 14295635051220, 37427619770555, 97989103308668, 256543448251865, 671648757639728, 1758417857052889, 4603634878290046, 12052546907359429, 31554126102872566, 82610071919426883, 216276570691745274, 566220602228483283, 1482387160139053224, 3880944726479373647, 10160454715880462192, 26600434814324801837, 69640880513419521092, 182322268298584916941, 477326047527637540690, 1249656120574932327001, 3271642806778368684010, 8565273284922592212375, 22424179018314244927758, 58707267710669816520135, 153697631994994552531068, 402385644036912536869859, 1053459331640940449672036, 2757992413936303595333249, 7220518036268759902701656, 18903561947071555245519553, 49490168309349064099352614, 129566943989781953583529453, 339210665677609429713218014, 888065057078271601680089067, 2324984513627655907574978082, 6086888499945597185540702907, 15935681018490937778038846032, 41720154620090820406559265911, 109224782970908731957605813080, 285954194550889792498191896021, 748637801198269479600837320300, 1959959210076936314432054955445, 5131239831098574799950797327098, 13433760287350858757931276587905, 35170041039218142818864911560658, 92076362846831852388707216342079, 241059047534333979727344253961526, 631100779822283217553500578534319, 1652243292064741934453507547624996, 4325629096636395108847722196307723, 11324643998373348438171059305232204, 29648302899541460297828256247256873, 77620264702366652639639310492274304, 203212491211789737989740877341037737, 532017208941465042066885725753782222, 1392839135629530349685521108366195477, 3646500197980975929938887216236577222, 9546661458381097286029559774127082131, 24993484177297715619946630573711760970, 65433791073782848957404008882142384291, 171307889044592430019452749942983758840, 448489876061077638635328948687345626015, 1174161739140806880955283511600126586688, 3073995341365675794368020417075181068925, 8047824284964886082423775401549710489748, 21069477513546313613453301111422538139549, 55160608255708717079036118580415079407266, 144412347253649162265855035925217051038889, 378076433505377419002928951786024775622586
Generating function in Maple syntax:
(x^2+x-1)*(x^6-3*x^5+5*x^4-7*x^3+9*x^2-5*x+1)/(2*x-1)/(x^2-3*x+1)/(x-1)^2
Generating function in latex syntax:
\frac{\left(x^{2}+x -1\right) \left(x^{6}-3 x^{5}+5 x^{4}-7 x^{3}+9 x^{2}-5 x +1\right)}{\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(x**2 + x - 1)*(x**6 - 3*x**5 + 5*x**4 - 7*x**3 + 9*x**2 - 5*x + 1)/((x - 1)**2*(2*x - 1)*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
-(2*x-1)*(x^2-3*x+1)*(x-1)^2*F(x)+(x^2+x-1)*(x^6-3*x^5+5*x^4-7*x^3+9*x^2-5*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 -1\right)^{2} F \! \left(x \right)+\left(x^{2}+x -1\right) \left(x^{6}-3 x^{5}+5 x^{4}-7 x^{3}+9 x^{2}-5 x +1\right) = 0
Explicit closed form in Maple syntax:
1/2*piecewise(n = 0,215/8,n = 1,39/4,n = 2,7/2,n = 3,1,0)-n+2+17/5*(3/2-1/2*5^(1/2))^(-n)*5^(1/2)-17/5*(3/2+1/2*5^(1/2))^(-n)*5^(1/2)-7/16*2^n-7*(3/2-1/2*5^(1/2))^(-n)-7*(3/2+1/2*5^(1/2))^(-n)
Explicit closed form in latex syntax:
\frac{\left(\left\{\begin{array}{cc}\frac{215}{8} & n =0 \\ \frac{39}{4} & n =1 \\ \frac{7}{2} & n =2 \\ 1 & n =3 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)}{2}-n +2+\frac{17 \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}}{5}-\frac{17 \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}}{5}-\frac{7 \,2^{n}}{16}-7 \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}-7 \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 57
a(6) = 162
a(7) = 447
a(8) = 1212
a(n+3) = 2*a(n)-7*a(n+1)+5*a(n+2)+2-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) = 57
a \! \left(6\right) = 162
a \! \left(7\right) = 447
a \! \left(8\right) = 1212
a \! \left(n +3\right) = 2 a \! \left(n \right)-7 a \! \left(n +1\right)+5 a \! \left(n +2\right)+2-n, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16096/
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[17,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[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[7,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[4,x]
F[14,x] = F[15,x]+F[16,x]
F[15,x] = F[4,x]
F[16,x] = F[12,x]
F[17,x] = F[18,x]+F[54,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[24,x]
F[21,x] = F[1,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[10,x]*F[4,x]
F[24,x] = F[18,x]+F[25,x]
F[25,x] = F[26,x]+F[27,x]+F[52,x]
F[26,x] = 0
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[22,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[15,x]*F[4,x]
F[32,x] = F[25,x]+F[33,x]
F[33,x] = 2*F[26,x]+F[34,x]+F[38,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[30,x]
F[37,x] = F[33,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]
F[40,x] = F[26,x]+F[41,x]+F[51,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]+F[45,x]
F[43,x] = F[4,x]+F[44,x]
F[44,x] = F[31,x]
F[45,x] = F[40,x]+F[46,x]
F[46,x] = 2*F[26,x]+F[38,x]+F[47,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[44,x]
F[50,x] = F[46,x]
F[51,x] = F[18,x]*F[4,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[18,x]+F[40,x]
F[54,x] = F[26,x]+F[55,x]+F[89,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[57,x]+F[61,x]
F[57,x] = F[22,x]+F[58,x]
F[58,x] = F[26,x]+F[31,x]+F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[22,x]+F[44,x]
F[61,x] = F[62,x]+F[81,x]
F[62,x] = F[26,x]+F[55,x]+F[63,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[18,x]+F[65,x]
F[65,x] = F[26,x]+F[51,x]+F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[71,x]
F[68,x] = F[4,x]+F[69,x]
F[69,x] = F[26,x]+F[31,x]+F[70,x]
F[70,x] = F[22,x]*F[4,x]
F[71,x] = F[65,x]+F[72,x]
F[72,x] = F[26,x]+F[73,x]+F[78,x]+F[80,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = F[44,x]
F[76,x] = F[77,x]
F[77,x] = 2*F[26,x]+F[73,x]+F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[65,x]
F[80,x] = F[25,x]*F[4,x]
F[81,x] = F[26,x]+F[78,x]+F[82,x]+F[87,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[30,x]
F[85,x] = F[86,x]
F[86,x] = 2*F[26,x]+F[78,x]+F[82,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[25,x]+F[77,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[64,x]+F[91,x]
F[91,x] = F[100,x]+F[92,x]
F[92,x] = F[26,x]+F[27,x]+F[93,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[53,x]+F[95,x]
F[95,x] = F[92,x]+F[96,x]
F[96,x] = 2*F[26,x]+F[47,x]+F[97,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[39,x]+F[99,x]
F[99,x] = F[96,x]
F[100,x] = 2*F[26,x]+F[101,x]+F[73,x]
F[101,x] = F[102,x]*F[4,x]
F[102,x] = F[103,x]+F[79,x]
F[103,x] = F[100,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_{17}\! \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_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{7}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)
F_{15}\! \left(x \right) = F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{12}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{54}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{24}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{18}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)+F_{52}\! \left(x \right)
F_{26}\! \left(x \right) = 0
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = F_{22}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{25}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
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_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)
F_{37}\! \left(x \right) = F_{33}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{26}\! \left(x \right)+F_{41}\! \left(x \right)+F_{51}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{45}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{31}\! \left(x \right)
F_{45}\! \left(x \right) = F_{40}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{38}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{44}\! \left(x \right)
F_{50}\! \left(x \right) = F_{46}\! \left(x \right)
F_{51}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{18}\! \left(x \right)+F_{40}\! \left(x \right)
F_{54}\! \left(x \right) = F_{26}\! \left(x \right)+F_{55}\! \left(x \right)+F_{89}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{61}\! \left(x \right)
F_{57}\! \left(x \right) = F_{22}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{26}\! \left(x \right)+F_{31}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{22}\! \left(x \right)+F_{44}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{81}\! \left(x \right)
F_{62}\! \left(x \right) = F_{26}\! \left(x \right)+F_{55}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{18}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{26}\! \left(x \right)+F_{51}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{71}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{26}\! \left(x \right)+F_{31}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{71}\! \left(x \right) = F_{65}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{26}\! \left(x \right)+F_{73}\! \left(x \right)+F_{78}\! \left(x \right)+F_{80}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{44}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{73}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{65}\! \left(x \right)
F_{80}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{81}\! \left(x \right) = F_{26}\! \left(x \right)+F_{78}\! \left(x \right)+F_{82}\! \left(x \right)+F_{87}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{30}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{78}\! \left(x \right)+F_{82}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{25}\! \left(x \right)+F_{77}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{64}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{100}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{53}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{92}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{47}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{39}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{96}\! \left(x \right)
F_{100}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{101}\! \left(x \right)+F_{73}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{79}\! \left(x \right)
F_{103}\! \left(x \right) = F_{100}\! \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_17(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_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_7(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_4(x))
Eq(F_14(x), F_15(x) + F_16(x))
Eq(F_15(x), F_4(x))
Eq(F_16(x), F_12(x))
Eq(F_17(x), F_18(x) + F_54(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_24(x))
Eq(F_21(x), F_1(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_10(x)*F_4(x))
Eq(F_24(x), F_18(x) + F_25(x))
Eq(F_25(x), F_26(x) + F_27(x) + F_52(x))
Eq(F_26(x), 0)
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_22(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_15(x)*F_4(x))
Eq(F_32(x), F_25(x) + F_33(x))
Eq(F_33(x), 2*F_26(x) + F_34(x) + F_38(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_30(x))
Eq(F_37(x), F_33(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_26(x) + F_41(x) + F_51(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_45(x))
Eq(F_43(x), F_4(x) + F_44(x))
Eq(F_44(x), F_31(x))
Eq(F_45(x), F_40(x) + F_46(x))
Eq(F_46(x), 2*F_26(x) + F_38(x) + F_47(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_44(x))
Eq(F_50(x), F_46(x))
Eq(F_51(x), F_18(x)*F_4(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_18(x) + F_40(x))
Eq(F_54(x), F_26(x) + F_55(x) + F_89(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_61(x))
Eq(F_57(x), F_22(x) + F_58(x))
Eq(F_58(x), F_26(x) + F_31(x) + F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_22(x) + F_44(x))
Eq(F_61(x), F_62(x) + F_81(x))
Eq(F_62(x), F_26(x) + F_55(x) + F_63(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_18(x) + F_65(x))
Eq(F_65(x), F_26(x) + F_51(x) + F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_71(x))
Eq(F_68(x), F_4(x) + F_69(x))
Eq(F_69(x), F_26(x) + F_31(x) + F_70(x))
Eq(F_70(x), F_22(x)*F_4(x))
Eq(F_71(x), F_65(x) + F_72(x))
Eq(F_72(x), F_26(x) + F_73(x) + F_78(x) + F_80(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), F_44(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), 2*F_26(x) + F_73(x) + F_78(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_65(x))
Eq(F_80(x), F_25(x)*F_4(x))
Eq(F_81(x), F_26(x) + F_78(x) + F_82(x) + F_87(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_30(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), 2*F_26(x) + F_78(x) + F_82(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_25(x) + F_77(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_64(x) + F_91(x))
Eq(F_91(x), F_100(x) + F_92(x))
Eq(F_92(x), F_26(x) + F_27(x) + F_93(x))
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_53(x) + F_95(x))
Eq(F_95(x), F_92(x) + F_96(x))
Eq(F_96(x), 2*F_26(x) + F_47(x) + F_97(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_39(x) + F_99(x))
Eq(F_99(x), F_96(x))
Eq(F_100(x), F_101(x) + 2*F_26(x) + F_73(x))
Eq(F_101(x), F_102(x)*F_4(x))
Eq(F_102(x), F_103(x) + F_79(x))
Eq(F_103(x), F_100(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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "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, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}], "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, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "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, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}], "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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "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, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [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, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "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, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [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], "pos": [[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, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [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, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "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, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 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, 1], [0, 1], [0, 1]]}, {"patt": [0, 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