0132_0231_0321_1023_1203
Counting sequence:
1, 1, 2, 6, 19, 56, 161, 462, 1329, 3827, 11021, 31735, 91377, 263108, 757588, 2181388, 6281058, 18085587, 52075372, 149945056, 431749580, 1243173369, 3579575053, 10306975580, 29677753370, 85453685055, 246054079584, 708484485383, 2039999771096, 5873945233705, 16913351215731, 48700053876095, 140226216394579, 403765297968007, 1162595840027928, 3347561303689206, 9638918613099610, 27754159999270900, 79914918694123493, 230105837469270870, 662563352408541712, 1907775138531501644, 5493219578125234061, 15817095381967160469, 45543511007369979762, 131137313443984705226, 377594844949986955211, 1087241023842590885872, 3130585758083787952389, 9014162429301376901954, 25955246264061539819989, 74735153034100831507579, 215191296673001117620785, 619618643754941813042367, 1784120778230724607619521, 5137171038019172705237776, 14791894470302576302670960, 42591562632677004300393360, 122637516860011840195942306, 353120656109732944285155959, 1016770405696521828555074516, 2927673700229553645469281240, 8429900444578927992122687760, 24272930928040262147812988765, 69891119083891232797969685057, 201243456807094770401786367412, 579457439493244049057546113470, 1668481199395840914374668655351, 4804200141380427972722219598640, 13833142984648039869109112682451, 39830947754548278692952669392004, 114688643122264408106135788577373, 330232786382145184449298253049667, 950867411391887274654942089756995, 2737913591053397415858690480693611, 7883507986778047063126773189031167, 22699656548942253914725377477336508, 65361056055773364328317441951315914, 188199660180542045921825552664916574, 541899323992683883850751280517413212, 1560336915922278287223936399600923721, 4492811087586292815749983646137854590, 12936533938766194563399199657896150560, 37249264900376305402973662574087527960, 107254983613542623393171004076124729289, 308828416901861675616113812570478037305, 889235985805208721445367775137346583954, 2560452973802083540942932321335915022574, 7372530504504388947212683151437267030419, 21228355527707958120192681679174454507304, 61124613609321790819635112716187448499337, 176001310323460983511692654997125078467590, 506775575442674992414885283312200780895465, 1459202112718703186425020737220414894187059, 4201605027832648575763369556664119604093589, 12098039508055270734875223386680158031385303, 34834916411447109018200649422820059199968849, 100303144206508678478838578711796057995812956, 288811393111470764701640512748708015956053564, 831599262922965185086720888823303988668191844, 2394494644562386876781324087758115908008762578
Generating function in Maple syntax:
(2*x-1)*(x-1)/(x^2-x+1)/(x^3-3*x+1)
Generating function in latex syntax:
\frac{\left(2 x -1\right) \left(x -1\right)}{\left(x^{2}-x +1\right) \left(x^{3}-3 x +1\right)}
Generating function in sympy syntax:
(x - 1)*(2*x - 1)/((x**2 - x + 1)*(x**3 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
(x^2-x+1)*(x^3-3*x+1)*F(x)-(2*x-1)*(x-1) = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}-x +1\right) \left(x^{3}-3 x +1\right) F \! \left(x \right)-\left(2 x -1\right) \left(x -1\right) = 0
Explicit closed form in Maple syntax:
1/144*(I*3^(1/2)*(-4+4*I*3^(1/2))^(1/3)-(-4+4*I*3^(1/2))^(2/3)+(-4+4*I*3^(1/2))^(1/3)-4)*((I*3^(1/2)*(-4+4*I*3^(1/2))^(1/3)+(-4+4*I*3^(1/2))^(1/3)-(-4+4*I*3^(1/2))^(2/3)+4)*(1/2*(-4+4*I*3^(1/2))^(1/3)-1/8*(-4+4*I*3^(1/2))^(2/3)-1/8*I*(-4+4*I*3^(1/2))^(2/3)*3^(1/2))^(-n)-1/2*2^(3*n+3)*((-4+4*I*3^(1/2))^(1/3)*(-1+I*3^(1/2))*((-4+4*I*3^(1/2))^(1/3)+2))^(-n)+4^n*(-1+I*3^(1/2))*((-4+4*I*3^(1/2))^(1/3)+1/2*(-4+4*I*3^(1/2))^(2/3))*((-4+4*I*3^(1/2))^(1/3)*(-I*3^(1/2)+(-4+4*I*3^(1/2))^(1/3)-1))^(-n)+2*(I*3^(1/2)*(-4+4*I*3^(1/2))^(1/3)+1/4*(-4+4*I*3^(1/2))^(2/3)*(I*3^(1/2)-3))*((1/2-1/2*I*3^(1/2))^(-n)+(1/2+1/2*I*3^(1/2))^(-n)))
Explicit closed form in latex syntax:
\frac{\left(\mathrm{I} \sqrt{3}\, \left(-4+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}-\left(-4+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}}+\left(-4+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}-4\right) \left(\left(\mathrm{I} \sqrt{3}\, \left(-4+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}+\left(-4+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}-\left(-4+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}}+4\right) \left(\frac{\left(-4+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}}{2}-\frac{\left(-4+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}}}{8}-\frac{\mathrm{I} \left(-4+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}} \sqrt{3}}{8}\right)^{-n}-\frac{2^{3 n +3} \left(\left(-4+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}} \left(-1+\mathrm{I} \sqrt{3}\right) \left(\left(-4+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}+2\right)\right)^{-n}}{2}+4^{n} \left(-1+\mathrm{I} \sqrt{3}\right) \left(\left(-4+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}+\frac{\left(-4+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}}}{2}\right) \left(\left(-4+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}} \left(-\mathrm{I} \sqrt{3}+\left(-4+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}-1\right)\right)^{-n}+2 \left(\mathrm{I} \sqrt{3}\, \left(-4+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}+\frac{\left(-4+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}} \left(\mathrm{I} \sqrt{3}-3\right)}{4}\right) \left(\left(\frac{1}{2}-\frac{\mathrm{I} \sqrt{3}}{2}\right)^{-n}+\left(\frac{1}{2}+\frac{\mathrm{I} \sqrt{3}}{2}\right)^{-n}\right)\right)}{144}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(n+5) = -a(n)+a(n+1)+2*a(n+2)-4*a(n+3)+4*a(n+4), n >= 5
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(n +5\right) = -a \! \left(n \right)+a \! \left(n +1\right)+2 a \! \left(n +2\right)-4 a \! \left(n +3\right)+4 a \! \left(n +4\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18635/
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[18,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[11,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[4,x]
F[17,x] = F[15,x]
F[18,x] = F[19,x]+F[2,x]
F[19,x] = F[20,x]+F[21,x]+F[90,x]
F[20,x] = 0
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[33,x]
F[23,x] = F[24,x]+F[27,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[1,x]+F[4,x]
F[27,x] = F[20,x]+F[28,x]+F[31,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[16,x]+F[30,x]
F[30,x] = F[17,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[11,x]+F[17,x]
F[33,x] = F[34,x]+F[71,x]
F[34,x] = F[20,x]+F[21,x]+F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[2,x]+F[37,x]
F[37,x] = F[20,x]+F[38,x]+F[61,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[4,x]+F[41,x]
F[41,x] = F[20,x]+F[28,x]+F[42,x]
F[42,x] = F[11,x]*F[4,x]
F[43,x] = F[37,x]+F[44,x]
F[44,x] = F[20,x]+F[45,x]+F[63,x]+F[66,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]+F[52,x]
F[47,x] = F[48,x]+F[50,x]
F[48,x] = F[49,x]
F[49,x] = x^2
F[50,x] = F[51,x]
F[51,x] = F[17,x]*F[4,x]
F[52,x] = F[53,x]+F[55,x]
F[53,x] = 2*F[20,x]+F[45,x]+F[54,x]
F[54,x] = F[37,x]*F[4,x]
F[55,x] = F[56,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[60,x]+F[62,x]
F[60,x] = F[61,x]
F[61,x] = F[2,x]*F[4,x]
F[62,x] = F[58,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[59,x]+F[65,x]
F[65,x] = F[58,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[20,x]+F[38,x]+F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[2,x]+F[70,x]
F[70,x] = F[68,x]
F[71,x] = F[20,x]+F[63,x]+F[72,x]+F[88,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]+F[81,x]
F[74,x] = F[75,x]+F[78,x]
F[75,x] = F[76,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[4,x]
F[78,x] = F[79,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[17,x]
F[81,x] = F[82,x]+F[85,x]
F[82,x] = 2*F[20,x]+F[72,x]+F[83,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[37,x]
F[85,x] = F[86,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[57,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[57,x]+F[67,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[69,x]+F[92,x]
F[92,x] = F[67,x]+F[93,x]
F[93,x] = F[58,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_{18}\! \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_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{90}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{33}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{27}\! \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_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{20}\! \left(x \right)+F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{16}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{17}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{11}\! \left(x \right)+F_{17}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{71}\! \left(x \right)
F_{34}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{20}\! \left(x \right)+F_{38}\! \left(x \right)+F_{61}\! \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_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{20}\! \left(x \right)+F_{28}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{37}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{20}\! \left(x \right)+F_{45}\! \left(x \right)+F_{63}\! \left(x \right)+F_{66}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{52}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{50}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = x^{2}
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{55}\! \left(x \right)
F_{53}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{45}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{62}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{62}\! \left(x \right) = F_{58}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{59}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{58}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{20}\! \left(x \right)+F_{38}\! \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_{2}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{20}\! \left(x \right)+F_{63}\! \left(x \right)+F_{72}\! \left(x \right)+F_{88}\! \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_{81}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{78}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \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_{17}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{85}\! \left(x \right)
F_{82}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{72}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{37}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{57}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{57}\! \left(x \right)+F_{67}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{69}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{67}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{58}\! \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_18(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_11(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_4(x))
Eq(F_17(x), F_15(x))
Eq(F_18(x), F_19(x) + F_2(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_90(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_33(x))
Eq(F_23(x), F_24(x) + F_27(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_1(x) + F_4(x))
Eq(F_27(x), F_20(x) + F_28(x) + F_31(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_16(x) + F_30(x))
Eq(F_30(x), F_17(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_11(x) + F_17(x))
Eq(F_33(x), F_34(x) + F_71(x))
Eq(F_34(x), F_20(x) + F_21(x) + F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_2(x) + F_37(x))
Eq(F_37(x), F_20(x) + F_38(x) + F_61(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_4(x) + F_41(x))
Eq(F_41(x), F_20(x) + F_28(x) + F_42(x))
Eq(F_42(x), F_11(x)*F_4(x))
Eq(F_43(x), F_37(x) + F_44(x))
Eq(F_44(x), F_20(x) + F_45(x) + F_63(x) + F_66(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_52(x))
Eq(F_47(x), F_48(x) + F_50(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), x**2)
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_17(x)*F_4(x))
Eq(F_52(x), F_53(x) + F_55(x))
Eq(F_53(x), 2*F_20(x) + F_45(x) + F_54(x))
Eq(F_54(x), F_37(x)*F_4(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_62(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_2(x)*F_4(x))
Eq(F_62(x), F_58(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_59(x) + F_65(x))
Eq(F_65(x), F_58(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_20(x) + F_38(x) + F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_2(x) + F_70(x))
Eq(F_70(x), F_68(x))
Eq(F_71(x), F_20(x) + F_63(x) + F_72(x) + F_88(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_81(x))
Eq(F_74(x), F_75(x) + F_78(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_4(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_17(x))
Eq(F_81(x), F_82(x) + F_85(x))
Eq(F_82(x), 2*F_20(x) + F_72(x) + F_83(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_37(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_57(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_57(x) + F_67(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_69(x) + F_92(x))
Eq(F_92(x), F_67(x) + F_93(x))
Eq(F_93(x), F_58(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "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, 0], [0, 1], [0, 0]]}, {"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": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [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": [0, 1, 2], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"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": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [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": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "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, 0], [0, 1], [0, 0]]}, {"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": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "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, 0], [0, 1], [0, 0]]}, {"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": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "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], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": 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