0213_0321_1032_2130
Counting sequence:
1, 1, 2, 6, 20, 64, 194, 565, 1603, 4473, 12348, 33839, 92240, 250385, 677335, 1826938, 4915097, 13193417, 35343183, 94507677, 252300955, 672555842, 1790418134, 4760464692, 12643264427, 33544806348, 88916921393, 235488501342, 623176355798, 1647916241185, 4354783832672, 11500786059970, 30355547260240, 80078627751402, 211144611960546, 556472370581837, 1465958085849929, 3860351246869013, 10161816651390784, 26740292652527017, 70343080183619168, 184989216671828057, 486351132374381109, 1278321143386177806, 3359108143131513853, 8824881540351044747, 23179341157360123391, 60870456913812016197, 159819900878242215305, 419545570025481844302, 1101174694891888796690, 2889792049784589258438, 7582535139444772076483, 19893154089890332235188, 52184062196077394333279, 136873870209992182552858, 358967246115266447748346, 941333875500578188554555, 2468254434573666752612760, 6471368701189463352029282, 16965426512029208344555694, 44473174004752491336323174, 116573091785380282925987302, 305539495163828233337745871, 800768777049666823327865849, 2098550389146678533912496725, 5499279867755901563961446358, 14410131507806313032567749893, 37757847103061039996166256468, 98929320554638980789304758395, 259192622217970446016908429005, 679049220303613670062466832582, 1778942929484449618648996447523, 4660215283265688470728789733823, 12207708349431557598925058664851, 31977716578299722286811306919031, 83761948638303711932162916839873, 219398140568958959804632117029694, 574654402173595053190576616199680, 1505112247968684319139659256465818, 3942031457971823592059295363315775, 10324308468135024268625525595319638, 27039095280039946379129689994092071, 70813198344188511535569367493912570, 185450355999871602503001558343736192, 485660793784611961237036001141221799, 1271835103550587960885810959536044276, 3330591777749756356639480904840010604, 8721782654633537447311247373007584374, 22839298816067130201346417092779973638, 59807313971206481635200801411722571900, 156610257933330026552722244629033314675, 410091546173450125672623442525800175309, 1073832252319713787256865228236001263087, 2811819110500465480561952045540562519206, 7362645578411312031275296925532220061829, 19278633738276197208704415218713340360522, 50479459293584361825760264005579179671695, 132175039701120472345602173511063101088713, 346083372099144160150859296467880568149512, 906168058932063754173865837913380005360659
Generating function in Maple syntax:
(x^8-9*x^7+32*x^6-68*x^5+87*x^4-70*x^3+34*x^2-9*x+1)/(x^2-3*x+1)/(3*x^3-5*x^2+4*x-1)/(x-1)^3
Generating function in latex syntax:
\frac{x^{8}-9 x^{7}+32 x^{6}-68 x^{5}+87 x^{4}-70 x^{3}+34 x^{2}-9 x +1}{\left(x^{2}-3 x +1\right) \left(3 x^{3}-5 x^{2}+4 x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(x**8 - 9*x**7 + 32*x**6 - 68*x**5 + 87*x**4 - 70*x**3 + 34*x**2 - 9*x + 1)/((x - 1)**3*(x**2 - 3*x + 1)*(3*x**3 - 5*x**2 + 4*x - 1))
Implicit equation for the generating function in Maple syntax:
(x^2-3*x+1)*(3*x^3-5*x^2+4*x-1)*(x-1)^3*F(x)-x^8+9*x^7-32*x^6+68*x^5-87*x^4+70*x^3-34*x^2+9*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}-3 x +1\right) \left(3 x^{3}-5 x^{2}+4 x -1\right) \left(x -1\right)^{3} F \! \left(x \right)-x^{8}+9 x^{7}-32 x^{6}+68 x^{5}-87 x^{4}+70 x^{3}-34 x^{2}+9 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/1350360*(11470*((-42/1147*31^(1/2)+I)*3^(1/2)-126/1147*I*31^(1/2)+1)*2^(1/3)*(47+9*31^(1/2)*3^(1/2))^(2/3)-600160+8525*2^(2/3)*((69/155*31^(1/2)+I)*3^(1/2)-207/155*I*31^(1/2)-1)*(47+9*31^(1/2)*3^(1/2))^(1/3))*(47/8712*2^(1/3)*((I-9/47*31^(1/2))*3^(1/2)-27/47*I*31^(1/2)+1)*(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*(-8525*2^(2/3)*((-69/155*31^(1/2)+I)*3^(1/2)-207/155*I*31^(1/2)+1)*(47+9*31^(1/2)*3^(1/2))^(1/3)-600160-11470*((42/1147*31^(1/2)+I)*3^(1/2)-126/1147*I*31^(1/2)-1)*2^(1/3)*(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*((-7590*3^(1/2)*2^(2/3)*31^(1/2)+17050*2^(2/3))*(47+9*31^(1/2)*3^(1/2))^(1/3)-600160+(840*2^(1/3)*3^(1/2)*31^(1/2)-22940*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)+1/1350360*(270072*5^(1/2)+1350360)*(3/2-1/2*5^(1/2))^(-n)+1/1350360*(-270072*5^(1/2)+1350360)*(3/2+1/2*5^(1/2))^(-n)-1/2*n^2+1/2*n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(11470 \left(\left(-\frac{42 \sqrt{31}}{1147}+\mathrm{I}\right) \sqrt{3}-\frac{126 \,\mathrm{I} \sqrt{31}}{1147}+1\right) 2^{\frac{1}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}-600160+8525 \,2^{\frac{2}{3}} \left(\left(\frac{69 \sqrt{31}}{155}+\mathrm{I}\right) \sqrt{3}-\frac{207 \,\mathrm{I} \sqrt{31}}{155}-1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{47 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}-\frac{9 \sqrt{31}}{47}\right) \sqrt{3}-\frac{27 \,\mathrm{I} \sqrt{31}}{47}+1\right) \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(-8525 \,2^{\frac{2}{3}} \left(\left(-\frac{69 \sqrt{31}}{155}+\mathrm{I}\right) \sqrt{3}-\frac{207 \,\mathrm{I} \sqrt{31}}{155}+1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}-600160-11470 \left(\left(\frac{42 \sqrt{31}}{1147}+\mathrm{I}\right) \sqrt{3}-\frac{126 \,\mathrm{I} \sqrt{31}}{1147}-1\right) 2^{\frac{1}{3}} \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(-7590 \sqrt{3}\, 2^{\frac{2}{3}} \sqrt{31}+17050 \,2^{\frac{2}{3}}\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}-600160+\left(840 \,2^{\frac{1}{3}} \sqrt{3}\, \sqrt{31}-22940 \,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{\left(270072 \sqrt{5}+1350360\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{1350360}+\\\frac{\left(-270072 \sqrt{5}+1350360\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{1350360}-\frac{n^{2}}{2}+\frac{n}{2} & \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) = 64
a(6) = 194
a(7) = 565
a(8) = 1603
a(n+5) = 3*a(n)-14*a(n+1)+22*a(n+2)-18*a(n+3)+7*a(n+4)-1/2*n*(n+1), n >= 9
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 20
a \! \left(5\right) = 64
a \! \left(6\right) = 194
a \! \left(7\right) = 565
a \! \left(8\right) = 1603
a \! \left(n +5\right) = 3 a \! \left(n \right)-14 a \! \left(n +1\right)+22 a \! \left(n +2\right)-18 a \! \left(n +3\right)+7 a \! \left(n +4\right)-\frac{n \left(n +1\right)}{2}, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15733/
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[12,x]*F[4,x]
F[4,x] = F[17,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[5,x]+F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[13,x]
F[12,x] = x
F[13,x] = F[1,x]+F[10,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[9,x]
F[17,x] = F[18,x]+F[32,x]
F[18,x] = F[19,x]
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[21,x]+F[5,x]
F[21,x] = F[18,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[12,x]*F[24,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[12,x]*F[28,x]
F[28,x] = F[18,x]+F[26,x]
F[29,x] = F[30,x]
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[25,x]
F[32,x] = F[33,x]+F[34,x]+F[61,x]
F[33,x] = 0
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[36,x]+F[47,x]
F[36,x] = F[10,x]+F[37,x]
F[37,x] = F[33,x]+F[38,x]+F[42,x]
F[38,x] = F[12,x]*F[39,x]
F[39,x] = F[36,x]+F[40,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[42,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[10,x]+F[41,x]
F[44,x] = F[45,x]
F[45,x] = F[12,x]*F[46,x]
F[46,x] = F[40,x]
F[47,x] = F[48,x]+F[51,x]
F[48,x] = F[33,x]+F[34,x]+F[49,x]
F[49,x] = F[12,x]*F[50,x]
F[50,x] = F[18,x]+F[48,x]
F[51,x] = 2*F[33,x]+F[52,x]+F[56,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[47,x]+F[54,x]
F[54,x] = F[55,x]+F[58,x]
F[55,x] = F[56,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[26,x]+F[55,x]
F[58,x] = F[59,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = F[54,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[17,x]+F[63,x]
F[63,x] = F[64,x]+F[78,x]
F[64,x] = F[27,x]+F[33,x]+F[65,x]
F[65,x] = F[12,x]*F[66,x]
F[66,x] = F[36,x]+F[67,x]
F[67,x] = F[26,x]+F[68,x]
F[68,x] = 2*F[33,x]+F[69,x]+F[73,x]
F[69,x] = F[12,x]*F[70,x]
F[70,x] = F[67,x]+F[71,x]
F[71,x] = F[72,x]+F[75,x]
F[72,x] = F[73,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[26,x]+F[72,x]
F[75,x] = F[76,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[71,x]
F[78,x] = F[79,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[63,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{17}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{5}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{9}\! \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_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{5}\! \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_{12}\! \left(x \right) F_{24}\! \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_{12}\! \left(x \right) F_{28}\! \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_{12}\! \left(x \right) F_{31}\! \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_{61}\! \left(x \right)
F_{33}\! \left(x \right) = 0
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{47}\! \left(x \right)
F_{36}\! \left(x \right) = F_{10}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{33}\! \left(x \right)+F_{38}\! \left(x \right)+F_{42}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{36}\! \left(x \right)+F_{40}\! \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_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{10}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{40}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{48}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{18}\! \left(x \right)+F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{52}\! \left(x \right)+F_{56}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{47}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{58}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{26}\! \left(x \right)+F_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{54}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{17}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{78}\! \left(x \right)
F_{64}\! \left(x \right) = F_{27}\! \left(x \right)+F_{33}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{36}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{26}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{69}\! \left(x \right)+F_{73}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{67}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{75}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{26}\! \left(x \right)+F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{71}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{63}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_17(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_5(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_13(x))
Eq(F_12(x), x)
Eq(F_13(x), F_1(x) + F_10(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_9(x))
Eq(F_17(x), F_18(x) + F_32(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_21(x) + F_5(x))
Eq(F_21(x), F_18(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_12(x)*F_24(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_12(x)*F_28(x))
Eq(F_28(x), F_18(x) + F_26(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_25(x))
Eq(F_32(x), F_33(x) + F_34(x) + F_61(x))
Eq(F_33(x), 0)
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_47(x))
Eq(F_36(x), F_10(x) + F_37(x))
Eq(F_37(x), F_33(x) + F_38(x) + F_42(x))
Eq(F_38(x), F_12(x)*F_39(x))
Eq(F_39(x), F_36(x) + F_40(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_10(x) + F_41(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_12(x)*F_46(x))
Eq(F_46(x), F_40(x))
Eq(F_47(x), F_48(x) + F_51(x))
Eq(F_48(x), F_33(x) + F_34(x) + F_49(x))
Eq(F_49(x), F_12(x)*F_50(x))
Eq(F_50(x), F_18(x) + F_48(x))
Eq(F_51(x), 2*F_33(x) + F_52(x) + F_56(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_47(x) + F_54(x))
Eq(F_54(x), F_55(x) + F_58(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_26(x) + F_55(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_54(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_17(x) + F_63(x))
Eq(F_63(x), F_64(x) + F_78(x))
Eq(F_64(x), F_27(x) + F_33(x) + F_65(x))
Eq(F_65(x), F_12(x)*F_66(x))
Eq(F_66(x), F_36(x) + F_67(x))
Eq(F_67(x), F_26(x) + F_68(x))
Eq(F_68(x), 2*F_33(x) + F_69(x) + F_73(x))
Eq(F_69(x), F_12(x)*F_70(x))
Eq(F_70(x), F_67(x) + F_71(x))
Eq(F_71(x), F_72(x) + F_75(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_26(x) + F_72(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_71(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_63(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": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"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]]}]]}], "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": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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[], "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": 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