0132_0213_0231_0312_2310
Counting sequence:
1, 1, 2, 6, 19, 55, 139, 319, 691, 1453, 3021, 6277, 13097, 27471, 57871, 122243, 258503, 546553, 1154361, 2434217, 5123437, 10762155, 22561675, 47206711, 98590939, 205550245, 427853509, 889232749, 1845540561, 3825259303, 7918908071, 16374633867, 33822948367, 69793310321, 143881508081, 296352860113, 609885486933, 1254130596803, 2576980540771, 5291399890047, 10857677525347, 22265110684765, 45629732797885, 93458488630741, 191315023529209, 391426139812735, 800444465375679, 1636073302517779, 3342515348860631, 6825768185691753, 13933011347674921, 28428972648315257, 57983845202978237, 118219490219105371, 240942580065000891, 490892359384115783, 999799117277037163, 2035627031572309653, 4143311657181763381, 8430738502438540477, 17149707381027889057, 34875875514358233175, 70904672533322276695, 144115188075857138971, 292842062170140482079, 594907496377134477025, 1208261736827977159649, 2453416961803371989409, 4980620899901580660901, 10108815752392836114803, 20512779409965023335571, 41615854630288750498447, 84412300881294910366707, 171185785004024641292621, 347093936490918925632301, 703632605947577139401253, 1426154677826632857237193, 2890088287516222873629103, 5855734438758360067982191, 11862584604968548779961507, 24027400664840754850606567, 48659264239488824285415385, 98527454298592277742222105, 199472760236413813830371401, 403781223751286144355905549, 817233854059489322105615115, 1653810521232812711002493419, 3346306668693293555591351639, 6769984589841923378359461371, 13694711684594519291076664453, 27698908379010383650873242021, 56016786777663457439190951437, 113271513594612295153275697777, 229018907267795350856344072071, 462989574692732222812278818311, 935882669699747487823744548523, 1891572380028061060045868735023, 3822758841313254288888502819153, 7724745845140772915370542677201, 15607948015310074505928166049137, 31532808680677206362230500389877
Generating function in Maple syntax:
-(2*x^9-11*x^8+16*x^7+3*x^6-28*x^5+48*x^4-48*x^3+27*x^2-8*x+1)/(2*x-1)^2/(-1+x)^5
Generating function in latex syntax:
-\frac{2 x^{9}-11 x^{8}+16 x^{7}+3 x^{6}-28 x^{5}+48 x^{4}-48 x^{3}+27 x^{2}-8 x +1}{\left(2 x -1\right)^{2} \left(-1+x \right)^{5}}
Generating function in sympy syntax:
(-2*x**9 + 11*x**8 - 16*x**7 - 3*x**6 + 28*x**5 - 48*x**4 + 48*x**3 - 27*x**2 + 8*x - 1)/((x - 1)**5*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^2*(-1+x)^5*F(x)+2*x^9-11*x^8+16*x^7+3*x^6-28*x^5+48*x^4-48*x^3+27*x^2-8*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{2} \left(-1+x \right)^{5} F \! \left(x \right)+2 x^{9}-11 x^{8}+16 x^{7}+3 x^{6}-28 x^{5}+48 x^{4}-48 x^{3}+27 x^{2}-8 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,1/24*(6*n-3)*2^n+1/12*n^4-1/6*n^3-13/12*n^2+19/6*n-1)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ \frac{\left(6 n -3\right) 2^{n}}{24}+\frac{n^{4}}{12}-\frac{n^{3}}{6}-\frac{13 n^{2}}{12}+\frac{19 n}{6}-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) = 19
a(5) = 55
a(6) = 139
a(7) = 319
a(8) = 691
a(9) = 1453
a(n+2) = 1/12*n^4-5/6*n^3-1/12*n^2-4*a(n)+4*a(n+1)+53/6*n-7, n >= 10
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) = 55
a \! \left(6\right) = 139
a \! \left(7\right) = 319
a \! \left(8\right) = 691
a \! \left(9\right) = 1453
a \! \left(n +2\right) = \frac{n^{4}}{12}-\frac{5 n^{3}}{6}-\frac{n^{2}}{12}-4 a \! \left(n \right)+4 a \! \left(n +1\right)+\frac{53 n}{6}-7, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18124/
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[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[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[37,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[14,x]+F[22,x]
F[22,x] = F[23,x]+F[24,x]+F[26,x]
F[23,x] = 0
F[24,x] = F[12,x]*F[25,x]
F[25,x] = F[22,x]+F[6,x]
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[28,x]+F[33,x]
F[28,x] = F[14,x]+F[29,x]
F[29,x] = F[23,x]+F[30,x]+F[32,x]
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[10,x]+F[29,x]
F[32,x] = F[12,x]*F[28,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[14,x]+F[34,x]
F[37,x] = F[23,x]+F[38,x]+F[79,x]
F[38,x] = F[12,x]*F[39,x]
F[39,x] = F[40,x]+F[50,x]
F[40,x] = F[41,x]+F[6,x]
F[41,x] = F[23,x]+F[42,x]+F[47,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[10,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[12,x]*F[44,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[13,x]+F[49,x]
F[49,x] = F[34,x]
F[50,x] = F[51,x]+F[60,x]
F[51,x] = F[23,x]+F[52,x]+F[54,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[51,x]+F[6,x]
F[54,x] = F[12,x]*F[55,x]
F[55,x] = F[28,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[23,x]+F[35,x]+F[58,x]
F[58,x] = F[12,x]*F[59,x]
F[59,x] = F[14,x]+F[57,x]
F[60,x] = F[23,x]+F[61,x]+F[63,x]+F[70,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[41,x]+F[60,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[29,x]+F[66,x]
F[66,x] = 2*F[23,x]+F[67,x]+F[69,x]
F[67,x] = F[12,x]*F[68,x]
F[68,x] = F[45,x]+F[66,x]
F[69,x] = F[12,x]*F[65,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[56,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = 2*F[23,x]+F[74,x]+F[76,x]
F[74,x] = F[12,x]*F[75,x]
F[75,x] = F[34,x]+F[73,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[34,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[18,x]+F[82,x]
F[82,x] = F[23,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[23,x]+F[42,x]+F[87,x]
F[87,x] = F[12,x]*F[13,x]
F[88,x] = F[29,x]+F[89,x]
F[89,x] = F[23,x]+F[63,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[56,x]
F[93,x] = F[12,x]*F[81,x]
F[94,x] = F[95,x]
F[95,x] = F[23,x]+F[35,x]+F[96,x]
F[96,x] = F[12,x]*F[97,x]
F[97,x] = F[105,x]+F[98,x]
F[98,x] = F[14,x]+F[99,x]
F[99,x] = F[100,x]+F[23,x]+F[35,x]
F[100,x] = F[101,x]*F[12,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]+F[12,x]
F[103,x] = F[104,x]
F[104,x] = F[102,x]*F[12,x]
F[105,x] = F[106,x]+F[57,x]
F[106,x] = F[107,x]+F[109,x]+F[23,x]+F[76,x]
F[107,x] = F[108,x]*F[12,x]
F[108,x] = F[106,x]+F[99,x]
F[109,x] = F[110,x]*F[12,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]+F[116,x]
F[112,x] = F[113,x]+F[115,x]+F[23,x]
F[113,x] = F[114,x]*F[12,x]
F[114,x] = F[112,x]+F[12,x]
F[115,x] = F[12,x]*F[14,x]
F[116,x] = 2*F[23,x]+F[117,x]+F[119,x]
F[117,x] = F[118,x]*F[12,x]
F[118,x] = F[103,x]+F[116,x]
F[119,x] = F[111,x]*F[12,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_{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_{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_{37}\! \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_{14}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)+F_{26}\! \left(x \right)
F_{23}\! \left(x \right) = 0
F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{22}\! \left(x \right)+F_{6}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{33}\! \left(x \right)
F_{28}\! \left(x \right) = F_{14}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right)+F_{30}\! \left(x \right)+F_{32}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{10}\! \left(x \right)+F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{14}\! \left(x \right)+F_{34}\! \left(x \right)
F_{37}\! \left(x \right) = F_{23}\! \left(x \right)+F_{38}\! \left(x \right)+F_{79}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{50}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{6}\! \left(x \right)
F_{41}\! \left(x \right) = F_{23}\! \left(x \right)+F_{42}\! \left(x \right)+F_{47}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{10}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{13}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{34}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{60}\! \left(x \right)
F_{51}\! \left(x \right) = F_{23}\! \left(x \right)+F_{52}\! \left(x \right)+F_{54}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{51}\! \left(x \right)+F_{6}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{28}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{23}\! \left(x \right)+F_{35}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{14}\! \left(x \right)+F_{57}\! \left(x \right)
F_{60}\! \left(x \right) = F_{23}\! \left(x \right)+F_{61}\! \left(x \right)+F_{63}\! \left(x \right)+F_{70}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{41}\! \left(x \right)+F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{29}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{67}\! \left(x \right)+F_{69}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{45}\! \left(x \right)+F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{56}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = 2 F_{23}\! \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_{34}\! \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_{34}\! \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_{18}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{23}\! \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_{23}\! \left(x \right)+F_{42}\! \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_{29}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{23}\! \left(x \right)+F_{63}\! \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_{56}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{81}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{23}\! \left(x \right)+F_{35}\! \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_{105}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{14}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{23}\! \left(x \right)+F_{35}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{12}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{12}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{102}\! \left(x \right) F_{12}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{57}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{109}\! \left(x \right)+F_{23}\! \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_{106}\! \left(x \right)+F_{99}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{12}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{116}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{115}\! \left(x \right)+F_{23}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{12}\! \left(x \right)
F_{114}\! \left(x \right) = F_{112}\! \left(x \right)+F_{12}\! \left(x \right)
F_{115}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{116}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{117}\! \left(x \right)+F_{119}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{12}\! \left(x \right)
F_{118}\! \left(x \right) = F_{103}\! \left(x \right)+F_{116}\! \left(x \right)
F_{119}\! \left(x \right) = F_{111}\! \left(x \right) F_{12}\! \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_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))
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) + F_37(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_14(x) + F_22(x))
Eq(F_22(x), F_23(x) + F_24(x) + F_26(x))
Eq(F_23(x), 0)
Eq(F_24(x), F_12(x)*F_25(x))
Eq(F_25(x), F_22(x) + F_6(x))
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_33(x))
Eq(F_28(x), F_14(x) + F_29(x))
Eq(F_29(x), F_23(x) + F_30(x) + F_32(x))
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_10(x) + F_29(x))
Eq(F_32(x), F_12(x)*F_28(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_14(x) + F_34(x))
Eq(F_37(x), F_23(x) + F_38(x) + F_79(x))
Eq(F_38(x), F_12(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_50(x))
Eq(F_40(x), F_41(x) + F_6(x))
Eq(F_41(x), F_23(x) + F_42(x) + F_47(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_10(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_12(x)*F_44(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_13(x) + F_49(x))
Eq(F_49(x), F_34(x))
Eq(F_50(x), F_51(x) + F_60(x))
Eq(F_51(x), F_23(x) + F_52(x) + F_54(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_51(x) + F_6(x))
Eq(F_54(x), F_12(x)*F_55(x))
Eq(F_55(x), F_28(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_23(x) + F_35(x) + F_58(x))
Eq(F_58(x), F_12(x)*F_59(x))
Eq(F_59(x), F_14(x) + F_57(x))
Eq(F_60(x), F_23(x) + F_61(x) + F_63(x) + F_70(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_41(x) + F_60(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_29(x) + F_66(x))
Eq(F_66(x), 2*F_23(x) + F_67(x) + F_69(x))
Eq(F_67(x), F_12(x)*F_68(x))
Eq(F_68(x), F_45(x) + F_66(x))
Eq(F_69(x), F_12(x)*F_65(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_56(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), 2*F_23(x) + F_74(x) + F_76(x))
Eq(F_74(x), F_12(x)*F_75(x))
Eq(F_75(x), F_34(x) + F_73(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_34(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_18(x) + F_82(x))
Eq(F_82(x), F_23(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_23(x) + F_42(x) + F_87(x))
Eq(F_87(x), F_12(x)*F_13(x))
Eq(F_88(x), F_29(x) + F_89(x))
Eq(F_89(x), F_23(x) + F_63(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_56(x))
Eq(F_93(x), F_12(x)*F_81(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_23(x) + F_35(x) + F_96(x))
Eq(F_96(x), F_12(x)*F_97(x))
Eq(F_97(x), F_105(x) + F_98(x))
Eq(F_98(x), F_14(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_23(x) + F_35(x))
Eq(F_100(x), F_101(x)*F_12(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x) + F_12(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_102(x)*F_12(x))
Eq(F_105(x), F_106(x) + F_57(x))
Eq(F_106(x), F_107(x) + F_109(x) + F_23(x) + F_76(x))
Eq(F_107(x), F_108(x)*F_12(x))
Eq(F_108(x), F_106(x) + F_99(x))
Eq(F_109(x), F_110(x)*F_12(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x) + F_116(x))
Eq(F_112(x), F_113(x) + F_115(x) + F_23(x))
Eq(F_113(x), F_114(x)*F_12(x))
Eq(F_114(x), F_112(x) + F_12(x))
Eq(F_115(x), F_12(x)*F_14(x))
Eq(F_116(x), F_117(x) + F_119(x) + 2*F_23(x))
Eq(F_117(x), F_118(x)*F_12(x))
Eq(F_118(x), F_103(x) + F_116(x))
Eq(F_119(x), F_111(x)*F_12(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, 1, 3], "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": [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, 1, 3], "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": [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, 1, 3], "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": [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, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "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], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 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], [0, 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": [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, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "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], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 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, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 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], [0, 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": [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, 0, 2], "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, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "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], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": 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