0123_0231_1302_2130_3102
Counting sequence:
1, 1, 2, 6, 19, 51, 118, 255, 543, 1165, 2536, 5600, 12510, 28188, 63910, 145557, 332630, 762122, 1749843, 4024642, 9270247, 21379570, 49359972, 114065904, 263807837, 610553499, 1413915295, 3276056879, 7594114979, 17610590572, 40852488179, 94796178921, 220025713664, 510800398421, 1186072202892, 2754494039561, 6397843141581, 14862023611319, 34527698718406, 80222532332858, 186405503693236, 433161706175638, 1006621765562884, 2339397632213063, 5437011560057428, 12636662158049436, 29370962939731153, 68267779970125340, 158680484002914053, 368841670636128900, 857361455128501146, 1992940770627799010, 4632659597285807395, 10768895755776898173, 25033182943480030045, 58192165116358409617, 135274521618264689865, 314463410366302532582, 731015338580227138553, 1699357687829322069027, 3950433739099776526982, 9183457065032836717655, 21348573174352127448082, 49628662671338182003939, 115371145808838520977547, 268202379415182112669809, 623488897613189050660980, 1449423856446004592835364, 3369477706782744080292314, 7833037411581264686753632, 18209506890648015654294514, 42331775981611671993244681, 98409056427215070005061474, 228772533913259522977326206, 531830084275339383503784927, 1236351880243472739739144646, 2874163283726516105541963891, 6681606730234976481360946854, 15532826614029438494157189216, 36109391886413015668129914468, 83944053603551420583112878521, 195146052536130217078589143023, 453659140056245922080377895019, 1054628764237118945352480909123, 2451712856209175594346101358463, 5699537762357895585155370723696, 13249811503189176053609691522063, 30802062169654355667831036810925, 71606081922129496647362302796188, 166463894244642726991900935673385, 386981503688071088012542057025256, 899622649754552396028652240116045, 2091368526647147917707704817170905, 4861841165150390406388214578724283, 11302407853971388494397611442802930, 26274907282380454017363560189862302, 61081742352588818328162572666187600, 141997810443456621161116009868626042, 330104834100532052278302046077355888, 767400584153190475708667894389005787, 1783989815473801429466178007336958592
Generating function in Maple syntax:
(2*x^11-5*x^10+2*x^9+4*x^8-9*x^7-8*x^6+18*x^5-24*x^4+29*x^3-20*x^2+7*x-1)/(2*x-1)/(x^3-2*x^2+3*x-1)/(x-1)^3
Generating function in latex syntax:
\frac{2 x^{11}-5 x^{10}+2 x^{9}+4 x^{8}-9 x^{7}-8 x^{6}+18 x^{5}-24 x^{4}+29 x^{3}-20 x^{2}+7 x -1}{\left(2 x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(2*x**11 - 5*x**10 + 2*x**9 + 4*x**8 - 9*x**7 - 8*x**6 + 18*x**5 - 24*x**4 + 29*x**3 - 20*x**2 + 7*x - 1)/((x - 1)**3*(2*x - 1)*(x**3 - 2*x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
-(2*x-1)*(x^3-2*x^2+3*x-1)*(x-1)^3*F(x)+2*x^11-5*x^10+2*x^9+4*x^8-9*x^7-8*x^6+18*x^5-24*x^4+29*x^3-20*x^2+7*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+2 x^{11}-5 x^{10}+2 x^{9}+4 x^{8}-9 x^{7}-8 x^{6}+18 x^{5}-24 x^{4}+29 x^{3}-20 x^{2}+7 x -1 = 0
Explicit closed form in Maple syntax:
12-27/2*n+5/2*n^2+10/23*Sum(_alpha^(2-n),_alpha = RootOf(2*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1))-22/23*Sum(_alpha^(1-n),_alpha = RootOf(2*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1))+38/23*Sum(_alpha^(-n),_alpha = RootOf(2*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1))-9/23*Sum(_alpha^(-n-1),_alpha = RootOf(2*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1))+piecewise(n = 0,-25/2,n = 1,-2,Or(n = 2,n = 3),3,n = 4,1,0)
Explicit closed form in latex syntax:
12-\frac{27 n}{2}+\frac{5 n^{2}}{2}+\frac{10 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(2 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{2-n}\right)}{23}-\frac{22 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(2 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{1-n}\right)}{23}+\frac{38 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(2 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{23}-\frac{9 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(2 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{23}+\left(\left\{\begin{array}{cc}-\frac{25}{2} & n =0 \\ -2 & n =1 \\ 3 & n =2\text{ or } n =3 \\ 1 & n =4 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 51
a(6) = 118
a(7) = 255
a(8) = 543
a(9) = 1165
a(10) = 2536
a(11) = 5600
a(n+4) = 5/2*n^2-2*a(n)+5*a(n+1)-8*a(n+2)+5*a(n+3)-27/2*n+7, n >= 12
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 51
a \! \left(6\right) = 118
a \! \left(7\right) = 255
a \! \left(8\right) = 543
a \! \left(9\right) = 1165
a \! \left(10\right) = 2536
a \! \left(11\right) = 5600
a \! \left(n +4\right) = \frac{5 n^{2}}{2}-2 a \! \left(n \right)+5 a \! \left(n +1\right)-8 a \! \left(n +2\right)+5 a \! \left(n +3\right)-\frac{27 n}{2}+7, \quad n \geq 12
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/17478/
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[23,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[18,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[10,x]+F[17,x]
F[17,x] = F[14,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[22,x]
F[21,x] = F[11,x]
F[22,x] = F[18,x]
F[23,x] = F[24,x]+F[36,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[1,x]+F[14,x]
F[28,x] = F[24,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[35,x]
F[32,x] = F[24,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[32,x]*F[4,x]
F[35,x] = F[29,x]
F[36,x] = F[37,x]+F[38,x]+F[83,x]
F[37,x] = 0
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[60,x]
F[40,x] = F[41,x]+F[7,x]
F[41,x] = F[37,x]+F[42,x]+F[49,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[48,x]
F[44,x] = F[11,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[11,x]+F[45,x]
F[48,x] = F[18,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[13,x]+F[51,x]
F[51,x] = F[52,x]+F[56,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[17,x]+F[55,x]
F[55,x] = F[52,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[22,x]+F[59,x]
F[59,x] = F[56,x]
F[60,x] = F[61,x]+F[78,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[66,x]
F[64,x] = F[65,x]+F[7,x]
F[65,x] = F[19,x]
F[66,x] = F[61,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]+F[77,x]
F[70,x] = F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]+F[75,x]
F[74,x] = F[11,x]+F[18,x]
F[75,x] = F[71,x]+F[76,x]
F[76,x] = F[68,x]
F[77,x] = F[76,x]
F[78,x] = F[79,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[81,x]+F[82,x]
F[81,x] = F[71,x]
F[82,x] = F[76,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[85,x]+F[96,x]
F[85,x] = F[24,x]+F[86,x]
F[86,x] = F[34,x]+F[37,x]+F[87,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[89,x]+F[94,x]
F[89,x] = F[11,x]+F[90,x]
F[90,x] = F[37,x]+F[42,x]+F[91,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[14,x]+F[93,x]
F[93,x] = F[91,x]
F[94,x] = F[71,x]+F[95,x]
F[95,x] = F[79,x]
F[96,x] = F[29,x]+F[97,x]
F[97,x] = F[68,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_{23}\! \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_{18}\! \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_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \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_{22}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{36}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{28}\! \left(x \right) = F_{24}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = F_{24}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)+F_{83}\! \left(x \right)
F_{37}\! \left(x \right) = 0
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_{60}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{7}\! \left(x \right)
F_{41}\! \left(x \right) = F_{37}\! \left(x \right)+F_{42}\! \left(x \right)+F_{49}\! \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_{48}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \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_{11}\! \left(x \right)+F_{45}\! \left(x \right)
F_{48}\! \left(x \right) = F_{18}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{13}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{56}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{17}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{52}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{22}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{56}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{78}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \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_{7}\! \left(x \right)
F_{65}\! \left(x \right) = F_{19}\! \left(x \right)
F_{66}\! \left(x \right) = F_{61}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{77}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \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) = F_{74}\! \left(x \right)+F_{75}\! \left(x \right)
F_{74}\! \left(x \right) = F_{11}\! \left(x \right)+F_{18}\! \left(x \right)
F_{75}\! \left(x \right) = F_{71}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{68}\! \left(x \right)
F_{77}\! \left(x \right) = F_{76}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{82}\! \left(x \right)
F_{81}\! \left(x \right) = F_{71}\! \left(x \right)
F_{82}\! \left(x \right) = F_{76}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{96}\! \left(x \right)
F_{85}\! \left(x \right) = F_{24}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)+F_{87}\! \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_{94}\! \left(x \right)
F_{89}\! \left(x \right) = F_{11}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{37}\! \left(x \right)+F_{42}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{14}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{91}\! \left(x \right)
F_{94}\! \left(x \right) = F_{71}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{79}\! \left(x \right)
F_{96}\! \left(x \right) = F_{29}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{68}\! \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_23(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_18(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_10(x) + F_17(x))
Eq(F_17(x), F_14(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_22(x))
Eq(F_21(x), F_11(x))
Eq(F_22(x), F_18(x))
Eq(F_23(x), F_24(x) + F_36(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_1(x) + F_14(x))
Eq(F_28(x), F_24(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_35(x))
Eq(F_32(x), F_24(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_32(x)*F_4(x))
Eq(F_35(x), F_29(x))
Eq(F_36(x), F_37(x) + F_38(x) + F_83(x))
Eq(F_37(x), 0)
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_60(x))
Eq(F_40(x), F_41(x) + F_7(x))
Eq(F_41(x), F_37(x) + F_42(x) + F_49(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_48(x))
Eq(F_44(x), F_11(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_11(x) + F_45(x))
Eq(F_48(x), F_18(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_13(x) + F_51(x))
Eq(F_51(x), F_52(x) + F_56(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_17(x) + F_55(x))
Eq(F_55(x), F_52(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_22(x) + F_59(x))
Eq(F_59(x), F_56(x))
Eq(F_60(x), F_61(x) + F_78(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_66(x))
Eq(F_64(x), F_65(x) + F_7(x))
Eq(F_65(x), F_19(x))
Eq(F_66(x), F_61(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_77(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_75(x))
Eq(F_74(x), F_11(x) + F_18(x))
Eq(F_75(x), F_71(x) + F_76(x))
Eq(F_76(x), F_68(x))
Eq(F_77(x), F_76(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_82(x))
Eq(F_81(x), F_71(x))
Eq(F_82(x), F_76(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_96(x))
Eq(F_85(x), F_24(x) + F_86(x))
Eq(F_86(x), F_34(x) + F_37(x) + F_87(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_94(x))
Eq(F_89(x), F_11(x) + F_90(x))
Eq(F_90(x), F_37(x) + F_42(x) + F_91(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_14(x) + F_93(x))
Eq(F_93(x), F_91(x))
Eq(F_94(x), F_71(x) + F_95(x))
Eq(F_95(x), F_79(x))
Eq(F_96(x), F_29(x) + F_97(x))
Eq(F_97(x), F_68(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, 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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": 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"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": [3, 1, 0, 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, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": 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{"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, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [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": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], 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"tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, 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