0123_0231_1302_2031_2103
Counting sequence:
1, 1, 2, 6, 19, 52, 135, 356, 957, 2579, 6921, 18535, 49657, 133124, 356934, 956894, 2565112, 6876253, 18433468, 49415680, 132471012, 355120477, 951986059, 2552030034, 6841338506, 18339873319, 49164490178, 131797370533, 353314907340, 947146551233, 2539056712113, 6806559086833, 18246637170581, 48914549045469, 131127346197910, 351518745553220, 942331497154408, 2526148780802178, 6771956240627307, 18153875842200572, 48665879752216772, 130460727650357100, 349731712355766413, 937540920016818121, 2513306473655658746, 6737529312753743550, 18061586088298631867, 48418474619099823256, 129797498014820902959, 347953764001104738628, 932774697003112293333, 2500529453581314934879, 6703277402696093772237, 17969765512316090426247, 48172327231713229581065, 129137640072642535501184, 346184854290218497217294, 928032704272163836155506, 2487817388673783180005256, 6669199620763070378216649, 17878411729124914709021264, 47927431195940018703606340, 128481136682827498492008264, 344424937272869334785349081, 923314818643534005726301931, 2475169948717575330324826530, 6635295081730754229859577418, 17787522365666848026034123959, 47683780150221960797719767630, 127827970791673551456999340317, 342673967232459157511479163932, 918620917562757259963655891769, 2462586805175635695945307753549, 6601562904875664689276533701965, 17697095060948392707603015106501, 47441367765341718364580561757661, 127178125432174146987413166560626, 340931898684800026456150351593684, 913950879098404764549649582741076, 2450067631181112025115939529728130, 6568002213951700647415456611464983, 17607127465978745782117660433444232, 47200187744258100248415482718521592, 126531583723578746524733708749196984, 339198686376934227819302201929090105, 909304581938916516226507195496524097, 2437612101528861186188215591673885842, 6534612137167376475542320253700936262, 17517617243708784669913035091816834019, 46960233821942494233185683829136776524, 125888328870954315641560966384271101479, 337474285285958740708538055243779704116, 904681905389450072132414490304847078653, 2425219892667001472487304024429233423995, 6501391807163175916868929067226561993329, 17428562068970358677789436615333115625127, 46721499765216123045360742264934959871193, 125248344164749049290994585716635692917852, 335758650617855696816315518562078229162758, 900082729368745312518559874604403334846342, 2412890682688507835724251055849903249669464
Generating function in Maple syntax:
(x-1)^2/(x^6-3*x^4-2*x^3+2*x^2-3*x+1)
Generating function in latex syntax:
\frac{\left(x -1\right)^{2}}{x^{6}-3 x^{4}-2 x^{3}+2 x^{2}-3 x +1}
Generating function in sympy syntax:
(x - 1)**2/(x**6 - 3*x**4 - 2*x**3 + 2*x**2 - 3*x + 1)
Implicit equation for the generating function in Maple syntax:
(x^6-3*x^4-2*x^3+2*x^2-3*x+1)*F(x)-(x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{6}-3 x^{4}-2 x^{3}+2 x^{2}-3 x +1\right) F \! \left(x \right)-\left(x -1\right)^{2} = 0
Explicit closed form in Maple syntax:
-142744/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n+4)-142744/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n+4)-142744/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n+4)-142744/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n+4)-142744/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n+4)-142744/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n+4)-306450/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n+3)-306450/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n+3)-306450/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n+3)-306450/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n+3)-306450/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n+3)-306450/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n+3)+178560/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n+2)+178560/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n+2)+178560/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n+2)+178560/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n+2)+178560/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n+2)+178560/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n+2)+772871/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n+1)+772871/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n+1)+772871/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n+1)+772871/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n+1)+772871/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n+1)+772871/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n+1)+629899/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n-1)+629899/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n-1)+629899/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n-1)+629899/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n-1)+629899/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n-1)+629899/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n-1)+1798880/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n)+1798880/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n)+1798880/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n)+1798880/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n)+1798880/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n)+1798880/10488197*RootOf(_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n)
Explicit closed form in latex syntax:
-\frac{142744 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{10488197}-\frac{142744 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +4}}{10488197}-\frac{142744 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +4}}{10488197}-\frac{142744 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +4}}{10488197}-\frac{142744 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +4}}{10488197}-\frac{142744 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +4}}{10488197}-\frac{306450 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{10488197}-\frac{306450 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{10488197}-\frac{306450 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{10488197}-\frac{306450 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{10488197}-\frac{306450 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{10488197}-\frac{306450 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +3}}{10488197}+\frac{178560 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{10488197}+\frac{178560 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{10488197}+\frac{178560 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{10488197}+\frac{178560 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{10488197}+\frac{178560 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{10488197}+\frac{178560 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{10488197}+\frac{772871 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{10488197}+\frac{772871 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{10488197}+\frac{772871 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{10488197}+\frac{772871 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{10488197}+\frac{772871 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{10488197}+\frac{772871 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{10488197}+\frac{629899 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{10488197}+\frac{629899 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{10488197}+\frac{629899 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{10488197}+\frac{629899 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{10488197}+\frac{629899 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{10488197}+\frac{629899 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{10488197}+\frac{1798880 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{10488197}+\frac{1798880 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{10488197}+\frac{1798880 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{10488197}+\frac{1798880 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{10488197}+\frac{1798880 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{10488197}+\frac{1798880 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{10488197}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 52
a(n) = 3*a(n+2)+2*a(n+3)-2*a(n+4)+3*a(n+5)-a(n+6), n >= 6
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) = 52
a \! \left(n \right) = 3 a \! \left(n +2\right)+2 a \! \left(n +3\right)-2 a \! \left(n +4\right)+3 a \! \left(n +5\right)-a \! \left(n +6\right), \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/17455/
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[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[11,x]
F[17,x] = F[18,x]+F[2,x]
F[18,x] = F[19,x]+F[20,x]+F[38,x]
F[19,x] = 0
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[24,x]
F[22,x] = F[23,x]+F[7,x]
F[23,x] = F[15,x]
F[24,x] = F[25,x]+F[35,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[2,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[33,x] = F[34,x]*F[4,x]
F[34,x] = F[29,x]
F[35,x] = F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[29,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[47,x]
F[40,x] = F[2,x]+F[41,x]
F[41,x] = F[19,x]+F[30,x]+F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = F[11,x]+F[14,x]
F[45,x] = F[29,x]+F[46,x]
F[46,x] = F[36,x]
F[47,x] = F[25,x]+F[48,x]
F[48,x] = F[33,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_{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_{11}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{2}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{38}\! \left(x \right)
F_{19}\! \left(x \right) = 0
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{24}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{7}\! \left(x \right)
F_{23}\! \left(x \right) = F_{15}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{35}\! \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_{2}\! \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_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{29}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{29}\! \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_{47}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{19}\! \left(x \right)+F_{30}\! \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_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{45}\! \left(x \right) = F_{29}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{36}\! \left(x \right)
F_{47}\! \left(x \right) = F_{25}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{33}\! \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_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_11(x))
Eq(F_17(x), F_18(x) + F_2(x))
Eq(F_18(x), F_19(x) + F_20(x) + F_38(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_24(x))
Eq(F_22(x), F_23(x) + F_7(x))
Eq(F_23(x), F_15(x))
Eq(F_24(x), F_25(x) + F_35(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_2(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))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_29(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_29(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_47(x))
Eq(F_40(x), F_2(x) + F_41(x))
Eq(F_41(x), F_19(x) + F_30(x) + F_42(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), F_11(x) + F_14(x))
Eq(F_45(x), F_29(x) + F_46(x))
Eq(F_46(x), F_36(x))
Eq(F_47(x), F_25(x) + F_48(x))
Eq(F_48(x), F_33(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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