0132_0231_0312_1230_2310
Counting sequence:
1, 1, 2, 6, 19, 56, 149, 364, 835, 1832, 3897, 8116, 16663, 33888, 68493, 137884, 276875, 555096, 1111809, 2225540, 4453343, 8909328, 17821717, 35646956, 71297939, 142600456, 285206089, 570418004, 1140842535, 2281692352, 4563392797, 9126794556, 18253599003, 36507208888, 73014429713, 146028872484, 292057759215, 584115533936, 1168231084709, 2336462187660, 4672924395043, 9345848811368, 18691697645657, 37383395315956, 74766790658359, 149533581345056, 299067162720429, 598134325473244, 1196268650981035, 2392537301998872, 4785074604036897, 9570149208115396, 19140298416274943, 38280596832596688, 76561193665242933, 153122387330538284, 306244774661131955, 612489549322322376, 1224979098644706409, 2449958197289477780, 4899916394579023943, 9799832789158119808, 19599665578316315197, 39199331156632709756, 78398662313265502779, 156797324626531092856, 313594649253062277169, 627189298506124650084, 1254378597012249400335, 2508757194024498905392, 5017514388048997920197, 10035028776097995954636, 20070057552195992028483, 40140115104391984181288, 80280230208783968492153, 160560460417567937119284, 321120920835135874379095, 642241841670271748904416, 1284483683340543497960909, 2568967366681086996079900, 5137934733362173992324043, 10275869466724347984818648, 20551738933448695969814337, 41103477866897391939812356, 82206955733794783879815199, 164413911467589567759827856, 328827822935179135519860309, 657655645870358271039932524, 1315311291740716542080084435, 2630622583481433084160395912, 5261245166962866168321026697, 10522490333925732336642296276, 21044980667851464673284843623, 42089961335702929346569946688, 84179922671405858693140161373, 168359845342811717386280599484, 336719690685623434772561484635, 673439381371246869545123264056, 1346878762742493739090246832209, 2693757525484987478180493978020, 5387515050969974956360988279343
Generating function in Maple syntax:
(x^6-x^5-4*x^4+8*x^3-10*x^2+5*x-1)/(2*x-1)/(-1+x)^4
Generating function in latex syntax:
\frac{x^{6}-x^{5}-4 x^{4}+8 x^{3}-10 x^{2}+5 x -1}{\left(2 x -1\right) \left(-1+x \right)^{4}}
Generating function in sympy syntax:
(x**6 - x**5 - 4*x**4 + 8*x**3 - 10*x**2 + 5*x - 1)/((x - 1)**4*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
-(2*x-1)*(-1+x)^4*F(x)+x^6-x^5-4*x^4+8*x^3-10*x^2+5*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right) \left(-1+x \right)^{4} F \! \left(x \right)+x^{6}-x^{5}-4 x^{4}+8 x^{3}-10 x^{2}+5 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,-5+17/4*2^n-n^2-5/3*n-1/3*n^3)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ -5+\frac{17 \,2^{n}}{4}-n^{2}-\frac{5 n}{3}-\frac{n^{3}}{3} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 56
a(6) = 149
a(n+1) = 1/3*n^3+2*a(n)-4/3*n+2, n >= 7
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) = 56
a \! \left(6\right) = 149
a \! \left(n +1\right) = \frac{n^{3}}{3}+2 a \! \left(n \right)-\frac{4 n}{3}+2, \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18608/
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[20,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[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[14,x]+F[17,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[1,x]+F[14,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[19,x]
F[19,x] = F[10,x]+F[17,x]
F[20,x] = F[21,x]+F[32,x]
F[21,x] = F[22,x]
F[22,x] = F[12,x]*F[23,x]
F[23,x] = F[16,x]+F[24,x]
F[24,x] = F[14,x]+F[25,x]
F[25,x] = F[26,x]+F[27,x]+F[29,x]
F[26,x] = 0
F[27,x] = F[12,x]*F[28,x]
F[28,x] = F[14,x]+F[25,x]
F[29,x] = F[12,x]*F[30,x]
F[30,x] = F[14,x]+F[31,x]
F[31,x] = F[29,x]
F[32,x] = F[26,x]+F[33,x]+F[79,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[35,x]+F[43,x]
F[35,x] = F[36,x]+F[6,x]
F[36,x] = F[18,x]+F[26,x]+F[37,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[13,x]+F[39,x]
F[39,x] = F[31,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[17,x]+F[40,x]
F[43,x] = F[44,x]+F[61,x]
F[44,x] = F[26,x]+F[45,x]+F[47,x]
F[45,x] = F[12,x]*F[46,x]
F[46,x] = F[44,x]+F[6,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[49,x]+F[54,x]
F[49,x] = F[14,x]+F[50,x]
F[50,x] = F[26,x]+F[51,x]+F[53,x]
F[51,x] = F[12,x]*F[52,x]
F[52,x] = F[10,x]+F[50,x]
F[53,x] = F[12,x]*F[49,x]
F[54,x] = F[25,x]+F[55,x]
F[55,x] = 2*F[26,x]+F[56,x]+F[58,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[17,x]+F[55,x]
F[58,x] = F[12,x]*F[59,x]
F[59,x] = F[50,x]+F[60,x]
F[60,x] = F[58,x]
F[61,x] = F[26,x]+F[58,x]+F[62,x]+F[64,x]
F[62,x] = F[12,x]*F[63,x]
F[63,x] = F[36,x]+F[61,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[54,x]+F[66,x]
F[66,x] = F[67,x]+F[73,x]
F[67,x] = 2*F[26,x]+F[68,x]+F[70,x]
F[68,x] = F[12,x]*F[69,x]
F[69,x] = F[31,x]+F[67,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[31,x]+F[72,x]
F[72,x] = F[70,x]
F[73,x] = 3*F[26,x]+F[74,x]+F[76,x]
F[74,x] = F[12,x]*F[75,x]
F[75,x] = F[40,x]+F[73,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[60,x]+F[78,x]
F[78,x] = F[76,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[81,x]+F[94,x]
F[81,x] = F[21,x]+F[82,x]
F[82,x] = F[26,x]+F[83,x]+F[93,x]
F[83,x] = F[12,x]*F[84,x]
F[84,x] = F[85,x]+F[88,x]
F[85,x] = F[10,x]+F[86,x]
F[86,x] = F[18,x]+F[26,x]+F[87,x]
F[87,x] = F[12,x]*F[13,x]
F[88,x] = F[50,x]+F[89,x]
F[89,x] = F[26,x]+F[58,x]+F[90,x]+F[92,x]
F[90,x] = F[12,x]*F[91,x]
F[91,x] = F[86,x]+F[89,x]
F[92,x] = F[12,x]*F[54,x]
F[93,x] = F[12,x]*F[81,x]
F[94,x] = F[100,x]+F[95,x]
F[95,x] = F[26,x]+F[29,x]+F[96,x]
F[96,x] = F[12,x]*F[97,x]
F[97,x] = F[98,x]+F[99,x]
F[98,x] = F[14,x]+F[31,x]
F[99,x] = F[25,x]+F[67,x]
F[100,x] = 2*F[26,x]+F[101,x]+F[58,x]
F[101,x] = F[102,x]*F[12,x]
F[102,x] = F[103,x]+F[105,x]
F[103,x] = F[104,x]+F[17,x]
F[104,x] = F[41,x]
F[105,x] = F[106,x]+F[55,x]
F[106,x] = 3*F[26,x]+F[107,x]+F[76,x]
F[107,x] = F[108,x]*F[12,x]
F[108,x] = F[104,x]+F[106,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_{20}\! \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_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{17}\! \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_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{32}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{16}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{14}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = 0
F_{27}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{14}\! \left(x \right)+F_{25}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{26}\! \left(x \right)+F_{33}\! \left(x \right)+F_{79}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{43}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{6}\! \left(x \right)
F_{36}\! \left(x \right) = F_{18}\! \left(x \right)+F_{26}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{13}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{31}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{17}\! \left(x \right)+F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{61}\! \left(x \right)
F_{44}\! \left(x \right) = F_{26}\! \left(x \right)+F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{44}\! \left(x \right)+F_{6}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{54}\! \left(x \right)
F_{49}\! \left(x \right) = F_{14}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{26}\! \left(x \right)+F_{51}\! \left(x \right)+F_{53}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{10}\! \left(x \right)+F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{49}\! \left(x \right)
F_{54}\! \left(x \right) = F_{25}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{56}\! \left(x \right)+F_{58}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{17}\! \left(x \right)+F_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{50}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{26}\! \left(x \right)+F_{58}\! \left(x \right)+F_{62}\! \left(x \right)+F_{64}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{36}\! \left(x \right)+F_{61}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{54}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{73}\! \left(x \right)
F_{67}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{68}\! \left(x \right)+F_{70}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{31}\! \left(x \right)+F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{31}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{70}\! \left(x \right)
F_{73}\! \left(x \right) = 3 F_{26}\! \left(x \right)+F_{74}\! \left(x \right)+F_{76}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{40}\! \left(x \right)+F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{60}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{76}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{94}\! \left(x \right)
F_{81}\! \left(x \right) = F_{21}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{26}\! \left(x \right)+F_{83}\! \left(x \right)+F_{93}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{88}\! \left(x \right)
F_{85}\! \left(x \right) = F_{10}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{18}\! \left(x \right)+F_{26}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{88}\! \left(x \right) = F_{50}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{26}\! \left(x \right)+F_{58}\! \left(x \right)+F_{90}\! \left(x \right)+F_{92}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{86}\! \left(x \right)+F_{89}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{81}\! \left(x \right)
F_{94}\! \left(x \right) = F_{100}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)+F_{99}\! \left(x \right)
F_{98}\! \left(x \right) = F_{14}\! \left(x \right)+F_{31}\! \left(x \right)
F_{99}\! \left(x \right) = F_{25}\! \left(x \right)+F_{67}\! \left(x \right)
F_{100}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{101}\! \left(x \right)+F_{58}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{12}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{105}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{17}\! \left(x \right)
F_{104}\! \left(x \right) = F_{41}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{55}\! \left(x \right)
F_{106}\! \left(x \right) = 3 F_{26}\! \left(x \right)+F_{107}\! \left(x \right)+F_{76}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{12}\! \left(x \right)
F_{108}\! \left(x \right) = F_{104}\! \left(x \right)+F_{106}\! \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_20(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_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_1(x) + F_14(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_12(x)*F_19(x))
Eq(F_19(x), F_10(x) + F_17(x))
Eq(F_20(x), F_21(x) + F_32(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_12(x)*F_23(x))
Eq(F_23(x), F_16(x) + F_24(x))
Eq(F_24(x), F_14(x) + F_25(x))
Eq(F_25(x), F_26(x) + F_27(x) + F_29(x))
Eq(F_26(x), 0)
Eq(F_27(x), F_12(x)*F_28(x))
Eq(F_28(x), F_14(x) + F_25(x))
Eq(F_29(x), F_12(x)*F_30(x))
Eq(F_30(x), F_14(x) + F_31(x))
Eq(F_31(x), F_29(x))
Eq(F_32(x), F_26(x) + F_33(x) + F_79(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_43(x))
Eq(F_35(x), F_36(x) + F_6(x))
Eq(F_36(x), F_18(x) + F_26(x) + F_37(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_13(x) + F_39(x))
Eq(F_39(x), F_31(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_17(x) + F_40(x))
Eq(F_43(x), F_44(x) + F_61(x))
Eq(F_44(x), F_26(x) + F_45(x) + F_47(x))
Eq(F_45(x), F_12(x)*F_46(x))
Eq(F_46(x), F_44(x) + F_6(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_54(x))
Eq(F_49(x), F_14(x) + F_50(x))
Eq(F_50(x), F_26(x) + F_51(x) + F_53(x))
Eq(F_51(x), F_12(x)*F_52(x))
Eq(F_52(x), F_10(x) + F_50(x))
Eq(F_53(x), F_12(x)*F_49(x))
Eq(F_54(x), F_25(x) + F_55(x))
Eq(F_55(x), 2*F_26(x) + F_56(x) + F_58(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_17(x) + F_55(x))
Eq(F_58(x), F_12(x)*F_59(x))
Eq(F_59(x), F_50(x) + F_60(x))
Eq(F_60(x), F_58(x))
Eq(F_61(x), F_26(x) + F_58(x) + F_62(x) + F_64(x))
Eq(F_62(x), F_12(x)*F_63(x))
Eq(F_63(x), F_36(x) + F_61(x))
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_54(x) + F_66(x))
Eq(F_66(x), F_67(x) + F_73(x))
Eq(F_67(x), 2*F_26(x) + F_68(x) + F_70(x))
Eq(F_68(x), F_12(x)*F_69(x))
Eq(F_69(x), F_31(x) + F_67(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_31(x) + F_72(x))
Eq(F_72(x), F_70(x))
Eq(F_73(x), 3*F_26(x) + F_74(x) + F_76(x))
Eq(F_74(x), F_12(x)*F_75(x))
Eq(F_75(x), F_40(x) + F_73(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_60(x) + F_78(x))
Eq(F_78(x), F_76(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_94(x))
Eq(F_81(x), F_21(x) + F_82(x))
Eq(F_82(x), F_26(x) + F_83(x) + F_93(x))
Eq(F_83(x), F_12(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_88(x))
Eq(F_85(x), F_10(x) + F_86(x))
Eq(F_86(x), F_18(x) + F_26(x) + F_87(x))
Eq(F_87(x), F_12(x)*F_13(x))
Eq(F_88(x), F_50(x) + F_89(x))
Eq(F_89(x), F_26(x) + F_58(x) + F_90(x) + F_92(x))
Eq(F_90(x), F_12(x)*F_91(x))
Eq(F_91(x), F_86(x) + F_89(x))
Eq(F_92(x), F_12(x)*F_54(x))
Eq(F_93(x), F_12(x)*F_81(x))
Eq(F_94(x), F_100(x) + F_95(x))
Eq(F_95(x), F_26(x) + F_29(x) + F_96(x))
Eq(F_96(x), F_12(x)*F_97(x))
Eq(F_97(x), F_98(x) + F_99(x))
Eq(F_98(x), F_14(x) + F_31(x))
Eq(F_99(x), F_25(x) + F_67(x))
Eq(F_100(x), F_101(x) + 2*F_26(x) + F_58(x))
Eq(F_101(x), F_102(x)*F_12(x))
Eq(F_102(x), F_103(x) + F_105(x))
Eq(F_103(x), F_104(x) + F_17(x))
Eq(F_104(x), F_41(x))
Eq(F_105(x), F_106(x) + F_55(x))
Eq(F_106(x), F_107(x) + 3*F_26(x) + F_76(x))
Eq(F_107(x), F_108(x)*F_12(x))
Eq(F_108(x), F_104(x) + F_106(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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 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, 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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 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, 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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 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, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 1, 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": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 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], "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, 0, 1], "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": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "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": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [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, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 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, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], 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