0213_0321_2130_3102
Counting sequence:
1, 1, 2, 6, 20, 61, 166, 414, 976, 2231, 5039, 11390, 25958, 59842, 139610, 329239, 783493, 1878098, 4527835, 10965098, 26648041, 64942366, 158618837, 388109684, 950993708, 2332950614, 5728528813, 14077113847, 34614253213, 85156271211, 209583718034, 515993483447, 1270718684772, 3130047666054, 7711356232540, 19000899930127, 46824076335072, 115400104212660, 284431194928933, 701093407947923, 1728211810786998, 4260261470685379, 10502442418189400, 25891448483409448, 63831067718911869, 157367758642327463, 387976847284236337, 956535410801619727, 2358307906152626841, 5814379559337154351, 14335373832755918955, 35344099040328617381, 87141821250613875444, 214851222449217328691, 529724702965062413211, 1306061407966560439828, 3220162273589696112773, 7939489141823401473868, 19575275380049274044544, 48264034545458115701136, 118998012534274178242780, 293397271204389723601091, 723390261091433889242298, 1783566996564352556985132, 4397505035648896124998832, 10842349025519095734128325, 26732558078466904692090963, 65910974623102717899496356, 162508099836401414201647094, 400675089785028339117691752, 987892562466485554635210942, 2435718657728146996516034949, 6005436202491529692169715605, 14806827437837409373873428912, 36507281170301567871944369375, 90011289015944089390435610448, 221929218358681297714688043737, 547182243531710550304517539012, 1349116692712870186380174514441, 3326343094932176298270668324802, 8201335420085894734352360622652, 20220975830474125649710659931556, 49856254599569193110920935015617, 122924143692775098976243733010605, 303078225637899348455614683691805, 747260940632874560586227795740945, 1842425050913216961620018834353238, 4542630148387973418164680182104821, 11200178102855993204815109521128820, 27614836706166877930292692866185012, 68086346523437708585580462820423408, 167871736407256909573286112383144357, 413899722201884699692085007808281808, 1020499244484657317730580445380930138, 2516113572437156383325614254882522569, 6203657226503352808013528166600774689, 15295558762426320797193219429285975350, 37712289604789427355832953051147624737, 92982336227115041975708046362740676380, 229254573052949749743850572092698814878, 565243479652907583621567902929831525597
Generating function in Maple syntax:
-(x^10+11*x^9-75*x^8+201*x^7-331*x^6+370*x^5-289*x^4+155*x^3-54*x^2+11*x-1)/(2*x-1)/(3*x^3-5*x^2+4*x-1)/(x-1)^6
Generating function in latex syntax:
-\frac{x^{10}+11 x^{9}-75 x^{8}+201 x^{7}-331 x^{6}+370 x^{5}-289 x^{4}+155 x^{3}-54 x^{2}+11 x -1}{\left(2 x -1\right) \left(3 x^{3}-5 x^{2}+4 x -1\right) \left(x -1\right)^{6}}
Generating function in sympy syntax:
(-x**10 - 11*x**9 + 75*x**8 - 201*x**7 + 331*x**6 - 370*x**5 + 289*x**4 - 155*x**3 + 54*x**2 - 11*x + 1)/((x - 1)**6*(2*x - 1)*(3*x**3 - 5*x**2 + 4*x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(3*x^3-5*x^2+4*x-1)*(x-1)^6*F(x)+x^10+11*x^9-75*x^8+201*x^7-331*x^6+370*x^5-289*x^4+155*x^3-54*x^2+11*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(3 x^{3}-5 x^{2}+4 x -1\right) \left(x -1\right)^{6} F \! \left(x \right)+x^{10}+11 x^{9}-75 x^{8}+201 x^{7}-331 x^{6}+370 x^{5}-289 x^{4}+155 x^{3}-54 x^{2}+11 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/1350360*(-2945*2^(1/3)*((I-51/589*31^(1/2))*3^(1/2)-153/589*I*31^(1/2)+1)*(47+9*31^(1/2)*3^(1/2))^(2/3)+300080+3410*2^(2/3)*((I-6/31*31^(1/2))*3^(1/2)+18/31*I*31^(1/2)-1)*(47+9*31^(1/2)*3^(1/2))^(1/3))*(47/8712*((I-9/47*31^(1/2))*3^(1/2)-27/47*I*31^(1/2)+1)*2^(1/3)*(47+9*31^(1/2)*3^(1/2))^(2/3)-1/36*I*3^(1/2)*(188+36*31^(1/2)*3^(1/2))^(1/3)+1/36*(188+36*31^(1/2)*3^(1/2))^(1/3)+5/9)^(-n)+1/1350360*(-3410*((I+6/31*31^(1/2))*3^(1/2)+18/31*I*31^(1/2)+1)*2^(2/3)*(47+9*31^(1/2)*3^(1/2))^(1/3)+300080+2945*2^(1/3)*((I+51/589*31^(1/2))*3^(1/2)-153/589*I*31^(1/2)-1)*(47+9*31^(1/2)*3^(1/2))^(2/3))*(-47/8712*((I+9/47*31^(1/2))*3^(1/2)-27/47*I*31^(1/2)-1)*2^(1/3)*(47+9*31^(1/2)*3^(1/2))^(2/3)+1/36*I*3^(1/2)*(188+36*31^(1/2)*3^(1/2))^(1/3)+1/36*(188+36*31^(1/2)*3^(1/2))^(1/3)+5/9)^(-n)+1/1350360*((1320*2^(2/3)*31^(1/2)*3^(1/2)+6820*2^(2/3))*(47+9*31^(1/2)*3^(1/2))^(1/3)+300080+(-510*31^(1/2)*3^(1/2)*2^(1/3)+5890*2^(1/3))*(47+9*31^(1/2)*3^(1/2))^(2/3))*(1/4356*2^(1/3)*(9*31^(1/2)*3^(1/2)-47)*(47+9*31^(1/2)*3^(1/2))^(2/3)-1/18*(188+36*31^(1/2)*3^(1/2))^(1/3)+5/9)^(-n)+1/120*n^5-3/8*n^3+1/2*n^2-32/15*n+3*2^(n-1)-1)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(-2945 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}-\frac{51 \sqrt{31}}{589}\right) \sqrt{3}-\frac{153 \,\mathrm{I} \sqrt{31}}{589}+1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}+300080+3410 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}-\frac{6 \sqrt{31}}{31}\right) \sqrt{3}+\frac{18 \,\mathrm{I} \sqrt{31}}{31}-1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{47 \left(\left(\mathrm{I}-\frac{9 \sqrt{31}}{47}\right) \sqrt{3}-\frac{27 \,\mathrm{I} \sqrt{31}}{47}+1\right) 2^{\frac{1}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{8712}-\frac{\mathrm{I} \sqrt{3}\, \left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{\left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{5}{9}\right)^{-n}}{1350360}\\+\\\frac{\left(-3410 \left(\left(\mathrm{I}+\frac{6 \sqrt{31}}{31}\right) \sqrt{3}+\frac{18 \,\mathrm{I} \sqrt{31}}{31}+1\right) 2^{\frac{2}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}+300080+2945 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}+\frac{51 \sqrt{31}}{589}\right) \sqrt{3}-\frac{153 \,\mathrm{I} \sqrt{31}}{589}-1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(-\frac{47 \left(\left(\mathrm{I}+\frac{9 \sqrt{31}}{47}\right) \sqrt{3}-\frac{27 \,\mathrm{I} \sqrt{31}}{47}-1\right) 2^{\frac{1}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{8712}+\frac{\mathrm{I} \sqrt{3}\, \left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{\left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{5}{9}\right)^{-n}}{1350360}\\+\\\frac{\left(\left(1320 \,2^{\frac{2}{3}} \sqrt{31}\, \sqrt{3}+6820 \,2^{\frac{2}{3}}\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}+300080+\left(-510 \sqrt{31}\, \sqrt{3}\, 2^{\frac{1}{3}}+5890 \,2^{\frac{1}{3}}\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{2^{\frac{1}{3}} \left(9 \sqrt{31}\, \sqrt{3}-47\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{4356}-\frac{\left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{18}+\frac{5}{9}\right)^{-n}}{1350360}\\+\frac{n^{5}}{120}-\frac{3 n^{3}}{8}+\frac{n^{2}}{2}-\frac{32 n}{15}+3 \,2^{n -1}-1 & \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) = 166
a(7) = 414
a(8) = 976
a(9) = 2231
a(10) = 5039
a(n+4) = 1/120*n^5-1/24*n^4-7/24*n^3+25/24*n^2-6*a(n)+13*a(n+1)-13*a(n+2)+6*a(n+3)-343/60*n+4, n >= 11
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) = 166
a \! \left(7\right) = 414
a \! \left(8\right) = 976
a \! \left(9\right) = 2231
a \! \left(10\right) = 5039
a \! \left(n +4\right) = \frac{n^{5}}{120}-\frac{n^{4}}{24}-\frac{7 n^{3}}{24}+\frac{25 n^{2}}{24}-6 a \! \left(n \right)+13 a \! \left(n +1\right)-13 a \! \left(n +2\right)+6 a \! \left(n +3\right)-\frac{343 n}{60}+4, \quad n \geq 11
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15753/
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[6,x]
F[10,x] = F[11,x]+F[14,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[11,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[18,x]+F[32,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[6,x]
F[21,x] = F[18,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[21,x]+F[25,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[18,x]+F[26,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[25,x]
F[32,x] = F[33,x]+F[34,x]+F[64,x]
F[33,x] = 0
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[36,x]+F[49,x]
F[36,x] = F[37,x]+F[7,x]
F[37,x] = F[33,x]+F[38,x]+F[40,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[36,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[10,x]+F[42,x]
F[42,x] = F[43,x]+F[46,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[11,x]+F[43,x]
F[46,x] = F[47,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[42,x]
F[49,x] = F[50,x]+F[61,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[53,x]+F[57,x]
F[53,x] = F[54,x]+F[7,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[53,x]
F[57,x] = F[50,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[57,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[49,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[17,x]+F[66,x]
F[66,x] = F[67,x]+F[77,x]
F[67,x] = F[27,x]+F[33,x]+F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[11,x]+F[71,x]
F[71,x] = F[33,x]+F[72,x]+F[74,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[70,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[11,x]+F[76,x]
F[76,x] = F[74,x]
F[77,x] = 2*F[33,x]+F[78,x]+F[86,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[14,x]+F[81,x]
F[81,x] = 2*F[33,x]+F[82,x]+F[84,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[80,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[42,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[66,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_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \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_{18}\! \left(x \right)+F_{32}\! \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_{6}\! \left(x \right)
F_{21}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{18}\! \left(x \right)+F_{26}\! \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_{25}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)+F_{64}\! \left(x \right)
F_{33}\! \left(x \right) = 0
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_{49}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{7}\! \left(x \right)
F_{37}\! \left(x \right) = F_{33}\! \left(x \right)+F_{38}\! \left(x \right)+F_{40}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{36}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{10}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{11}\! \left(x \right)+F_{43}\! \left(x \right)
F_{46}\! \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_{42}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{61}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{57}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{7}\! \left(x \right)
F_{54}\! \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_{53}\! \left(x \right)
F_{57}\! \left(x \right) = F_{50}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \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_{57}\! \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_{49}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{17}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{77}\! \left(x \right)
F_{67}\! \left(x \right) = F_{27}\! \left(x \right)+F_{33}\! \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_{70}\! \left(x \right) = F_{11}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{33}\! \left(x \right)+F_{72}\! \left(x \right)+F_{74}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{70}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{11}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{74}\! \left(x \right)
F_{77}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{78}\! \left(x \right)+F_{86}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{14}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{82}\! \left(x \right)+F_{84}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{80}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{42}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{66}\! \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_6(x))
Eq(F_10(x), F_11(x) + F_14(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_11(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))
Eq(F_17(x), F_18(x) + F_32(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_6(x))
Eq(F_21(x), F_18(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_21(x) + F_25(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_18(x) + F_26(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_25(x))
Eq(F_32(x), F_33(x) + F_34(x) + F_64(x))
Eq(F_33(x), 0)
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_49(x))
Eq(F_36(x), F_37(x) + F_7(x))
Eq(F_37(x), F_33(x) + F_38(x) + F_40(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_36(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_10(x) + F_42(x))
Eq(F_42(x), F_43(x) + F_46(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_11(x) + F_43(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_42(x))
Eq(F_49(x), F_50(x) + F_61(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_57(x))
Eq(F_53(x), F_54(x) + F_7(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_53(x))
Eq(F_57(x), F_50(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_57(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_49(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_17(x) + F_66(x))
Eq(F_66(x), F_67(x) + F_77(x))
Eq(F_67(x), F_27(x) + F_33(x) + F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_11(x) + F_71(x))
Eq(F_71(x), F_33(x) + F_72(x) + F_74(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_70(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_11(x) + F_76(x))
Eq(F_76(x), F_74(x))
Eq(F_77(x), 2*F_33(x) + F_78(x) + F_86(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_14(x) + F_81(x))
Eq(F_81(x), 2*F_33(x) + F_82(x) + F_84(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_80(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_42(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_66(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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [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": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [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": [], 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"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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 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