0123_0231_1032_3012
Counting sequence:
1, 1, 2, 6, 20, 61, 178, 509, 1440, 4046, 11310, 31483, 87322, 241431, 665630, 1830486, 5022248, 13750489, 37575490, 102500561, 279153660, 759118238, 2061447042, 5590803031, 15144456490, 40977469611, 110759167418, 299078774694, 806842167740, 2174764019701, 5857033753810, 15761772537893, 42385005885912, 113897975901806, 305866392139350, 820868880693811, 2201685820154938, 5901857610231999, 15811948531711190, 42340503517950966, 113321047100119760, 303150577483293073, 810603019374435682, 2166547543013157881, 5788234462759793460, 15457851342177345086, 41265211201410854058, 110117761678059931279, 293748120443144470090, 783326760066495355731, 2088172594391331697010, 5564812166597348158278, 14825186901235267946852, 39483896381122272766381, 105127022778338446435570, 279825585718499937706061, 744634455134775084096528, 1981003528194059595659534, 5268868654214492828696190, 14010154260242451986795371, 37244757079124873294974810, 98989054009175165291617383, 263034053091917604597057422, 698783112665085597157606806, 1856013658955346050832738680, 4928682978958465198553484361, 13085612248140580610509364098, 34735459561367357186806681889, 92187106853453201545725253740, 244617576455563298683980721886, 648974428465458137611237267410, 1721440411340904392231180504263, 4565442106805313430221632161642, 12106037110419117793770250305531, 32096027527236227245959393813290, 85080969178298043933382221984486, 225500292825899157227139869632268, 597581224047114705777620888538469, 1583373910740349541521520703369490, 4194770787700932385004751442102901, 11111498759518538430730366377151560, 29429176132795956892681435731455918, 77933821257537063386561572189316262, 206356211853877152699251086910688931, 546328795327612421868687475393238650, 1446228192985452274947050893746295311, 3827955859174702861935688082426964038, 10130841592320039525709442428801278774, 26808575465583606900777703553195601440, 70933702240043971518529432203175031041, 187664977013589687494942820624279279010, 496439748642236040144789948401122662473, 1313117382678609900634767553205518490532, 3472923220848557115667043378363262299006, 9184221630466460340393614054701327094010, 24285438900894057133688022537044065555711, 64210617412646011851165873337523850603658, 169756283127991647563121633067503082774179, 448749319003741637477639712859819206245090, 1186155065189523715644807530904480365020806, 3135014963451288155142372269036365567470260
Generating function in Maple syntax:
-(2*x-1)*(x^5-2*x^4-4*x^2+4*x-1)/(x-1)/(x^2-3*x+1)^2
Generating function in latex syntax:
-\frac{\left(2 x -1\right) \left(x^{5}-2 x^{4}-4 x^{2}+4 x -1\right)}{\left(x -1\right) \left(x^{2}-3 x +1\right)^{2}}
Generating function in sympy syntax:
(1 - 2*x)*(x**5 - 2*x**4 - 4*x**2 + 4*x - 1)/((x - 1)*(x**2 - 3*x + 1)**2)
Implicit equation for the generating function in Maple syntax:
(x-1)*(x^2-3*x+1)^2*F(x)+(2*x-1)*(x^5-2*x^4-4*x^2+4*x-1) = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(x^{2}-3 x +1\right)^{2} F \! \left(x \right)+\left(2 x -1\right) \left(x^{5}-2 x^{4}-4 x^{2}+4 x -1\right) = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/25*((5*n-64)*5^(1/2)-10*n+150)*(3/2-1/2*5^(1/2))^(-n)-2+1/25*((-5*n+64)*5^(1/2)-10*n+150)*(3/2+1/2*5^(1/2))^(-n))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{\left(\left(5 n -64\right) \sqrt{5}-10 n +150\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{25}-2+\\\frac{\left(\left(-5 n +64\right) \sqrt{5}-10 n +150\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{25} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 61
a(6) = 178
a(n+4) = -a(n)+6*a(n+1)-11*a(n+2)+6*a(n+3)-2, n >= 7
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) = 61
a \! \left(6\right) = 178
a \! \left(n +4\right) = -a \! \left(n \right)+6 a \! \left(n +1\right)-11 a \! \left(n +2\right)+6 a \! \left(n +3\right)-2, \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14988/
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[19,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[7,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[4,x]
F[18,x] = F[15,x]
F[19,x] = F[20,x]+F[37,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[10,x]+F[23,x]
F[23,x] = F[20,x]+F[24,x]
F[24,x] = F[25,x]+F[26,x]+F[36,x]
F[25,x] = 0
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[29,x]+F[4,x]
F[29,x] = F[30,x]
F[30,x] = F[11,x]*F[4,x]
F[31,x] = F[32,x]+F[34,x]
F[32,x] = F[25,x]+F[26,x]+F[33,x]
F[33,x] = F[20,x]*F[4,x]
F[34,x] = F[35,x]
F[35,x] = F[24,x]*F[4,x]
F[36,x] = F[23,x]*F[4,x]
F[37,x] = F[25,x]+F[38,x]+F[87,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[50,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[1,x]+F[4,x]
F[44,x] = F[25,x]+F[45,x]+F[48,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[4,x]+F[47,x]
F[47,x] = F[45,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[11,x]+F[47,x]
F[50,x] = F[51,x]+F[76,x]
F[51,x] = F[25,x]+F[38,x]+F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[20,x]+F[54,x]
F[54,x] = F[25,x]+F[33,x]+F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[57,x]+F[59,x]
F[57,x] = F[4,x]+F[58,x]
F[58,x] = F[25,x]+F[30,x]+F[45,x]
F[59,x] = F[54,x]+F[60,x]
F[60,x] = F[25,x]+F[35,x]+F[61,x]+F[74,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[63,x]+F[68,x]
F[63,x] = F[64,x]+F[66,x]
F[64,x] = F[65,x]
F[65,x] = x^2
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[47,x]
F[68,x] = F[69,x]+F[71,x]
F[69,x] = 2*F[25,x]+F[61,x]+F[70,x]
F[70,x] = F[4,x]*F[54,x]
F[71,x] = F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = 2*F[25,x]+F[61,x]+F[74,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[54,x]+F[73,x]
F[76,x] = F[25,x]+F[74,x]+F[77,x]+F[85,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[79,x]+F[82,x]
F[79,x] = F[80,x]+F[81,x]
F[80,x] = F[65,x]
F[81,x] = F[67,x]
F[82,x] = F[83,x]+F[84,x]
F[83,x] = 2*F[25,x]+F[70,x]+F[77,x]
F[84,x] = F[72,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[24,x]+F[73,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[89,x]+F[91,x]
F[89,x] = F[20,x]+F[90,x]
F[90,x] = F[25,x]+F[36,x]+F[55,x]
F[91,x] = F[101,x]+F[92,x]
F[92,x] = F[25,x]+F[26,x]+F[93,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[23,x]+F[95,x]
F[95,x] = F[92,x]+F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[100,x]+F[99,x]
F[99,x] = F[32,x]
F[100,x] = F[97,x]
F[101,x] = 2*F[25,x]+F[102,x]+F[61,x]
F[102,x] = F[103,x]*F[4,x]
F[103,x] = F[104,x]+F[105,x]
F[104,x] = F[54,x]
F[105,x] = F[106,x]
F[106,x] = 2*F[25,x]+F[102,x]+F[61,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_{19}\! \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_{7}\! \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_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{15}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{37}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{10}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{20}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{36}\! \left(x \right)
F_{25}\! \left(x \right) = 0
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_{29}\! \left(x \right)+F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{34}\! \left(x \right)
F_{32}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{25}\! \left(x \right)+F_{38}\! \left(x \right)+F_{87}\! \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_{50}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{44}\! \left(x \right) = F_{25}\! \left(x \right)+F_{45}\! \left(x \right)+F_{48}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{45}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{11}\! \left(x \right)+F_{47}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{76}\! \left(x \right)
F_{51}\! \left(x \right) = F_{25}\! \left(x \right)+F_{38}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{20}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{25}\! \left(x \right)+F_{33}\! \left(x \right)+F_{55}\! \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_{59}\! \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_{30}\! \left(x \right)+F_{45}\! \left(x \right)
F_{59}\! \left(x \right) = F_{54}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{25}\! \left(x \right)+F_{35}\! \left(x \right)+F_{61}\! \left(x \right)+F_{74}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{68}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{66}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = x^{2}
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{71}\! \left(x \right)
F_{69}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{61}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{61}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{54}\! \left(x \right)+F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{25}\! \left(x \right)+F_{74}\! \left(x \right)+F_{77}\! \left(x \right)+F_{85}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{82}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = F_{65}\! \left(x \right)
F_{81}\! \left(x \right) = F_{67}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{70}\! \left(x \right)+F_{77}\! \left(x \right)
F_{84}\! \left(x \right) = F_{72}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{24}\! \left(x \right)+F_{73}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{91}\! \left(x \right)
F_{89}\! \left(x \right) = F_{20}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{25}\! \left(x \right)+F_{36}\! \left(x \right)+F_{55}\! \left(x \right)
F_{91}\! \left(x \right) = F_{101}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \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_{23}\! \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) = 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_{100}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{32}\! \left(x \right)
F_{100}\! \left(x \right) = F_{97}\! \left(x \right)
F_{101}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{102}\! \left(x \right)+F_{61}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{4}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{105}\! \left(x \right)
F_{104}\! \left(x \right) = F_{54}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{102}\! \left(x \right)+F_{61}\! \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_19(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_7(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_4(x))
Eq(F_18(x), F_15(x))
Eq(F_19(x), F_20(x) + F_37(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_10(x) + F_23(x))
Eq(F_23(x), F_20(x) + F_24(x))
Eq(F_24(x), F_25(x) + F_26(x) + F_36(x))
Eq(F_25(x), 0)
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_29(x) + F_4(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_11(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_34(x))
Eq(F_32(x), F_25(x) + F_26(x) + F_33(x))
Eq(F_33(x), F_20(x)*F_4(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_24(x)*F_4(x))
Eq(F_36(x), F_23(x)*F_4(x))
Eq(F_37(x), F_25(x) + F_38(x) + F_87(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_50(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_1(x) + F_4(x))
Eq(F_44(x), F_25(x) + F_45(x) + F_48(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_4(x) + F_47(x))
Eq(F_47(x), F_45(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_11(x) + F_47(x))
Eq(F_50(x), F_51(x) + F_76(x))
Eq(F_51(x), F_25(x) + F_38(x) + F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_20(x) + F_54(x))
Eq(F_54(x), F_25(x) + F_33(x) + F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_59(x))
Eq(F_57(x), F_4(x) + F_58(x))
Eq(F_58(x), F_25(x) + F_30(x) + F_45(x))
Eq(F_59(x), F_54(x) + F_60(x))
Eq(F_60(x), F_25(x) + F_35(x) + F_61(x) + F_74(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_68(x))
Eq(F_63(x), F_64(x) + F_66(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), x**2)
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_47(x))
Eq(F_68(x), F_69(x) + F_71(x))
Eq(F_69(x), 2*F_25(x) + F_61(x) + F_70(x))
Eq(F_70(x), F_4(x)*F_54(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), 2*F_25(x) + F_61(x) + F_74(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_54(x) + F_73(x))
Eq(F_76(x), F_25(x) + F_74(x) + F_77(x) + F_85(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_82(x))
Eq(F_79(x), F_80(x) + F_81(x))
Eq(F_80(x), F_65(x))
Eq(F_81(x), F_67(x))
Eq(F_82(x), F_83(x) + F_84(x))
Eq(F_83(x), 2*F_25(x) + F_70(x) + F_77(x))
Eq(F_84(x), F_72(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_24(x) + F_73(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_91(x))
Eq(F_89(x), F_20(x) + F_90(x))
Eq(F_90(x), F_25(x) + F_36(x) + F_55(x))
Eq(F_91(x), F_101(x) + F_92(x))
Eq(F_92(x), F_25(x) + F_26(x) + F_93(x))
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_23(x) + F_95(x))
Eq(F_95(x), F_92(x) + F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_100(x) + F_99(x))
Eq(F_99(x), F_32(x))
Eq(F_100(x), F_97(x))
Eq(F_101(x), F_102(x) + 2*F_25(x) + F_61(x))
Eq(F_102(x), F_103(x)*F_4(x))
Eq(F_103(x), F_104(x) + F_105(x))
Eq(F_104(x), F_54(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_102(x) + 2*F_25(x) + F_61(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, 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, 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, 1, 2, 3], "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, 1, 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, 2, 3], "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, 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, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [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, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "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, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "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]]}], "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, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [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, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "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, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "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]]}], "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": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 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, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [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, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "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, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "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]]}], "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, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [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, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "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, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "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]]}], "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": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "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, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [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, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "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, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "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]]}], "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, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, 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