0132_0213_0231_1320_2310
Counting sequence:
1, 1, 2, 6, 19, 55, 142, 338, 765, 1681, 3632, 7772, 16535, 35043, 74050, 156086, 328257, 688869, 1442724, 3015808, 6292859, 13108887, 27264982, 56625466, 117443269, 243272825, 503320152, 1040191588, 2147488415, 4429190411, 9126811562, 18790488702, 38654713225, 79456903373, 163208766540, 335007459336, 687194778627, 1408749285439, 2886218036414, 5909875014018, 12094627921549, 24739011642337, 50577534896512, 103354093031276, 211106232554919, 431008558111795, 879609302246162, 1794402976557638, 3659174697267665, 7459086882863541, 15199648742408692, 30962247438207632, 63050394783224715, 128352589380099303, 261208778387531430, 531424756029763786, 1080863910568966997, 2197756618156852809, 4467570830351585704, 9079256848778976628, 18446744073709611439, 37469948899722589787, 76092819304051966842, 154491481617317564686, 313594649253062450969, 636412670542979607965, 1291272085159668694172, 2619437658466756414488, 5312662293228350954515, 10772898539046378237071, 21840944983272109211022, 44272185776902923980562, 89724963174523259167005, 181811109590481340838833, 368344585663832326784720, 746133904293403943885436, 1511157274518286468509367, 3060093480899530098606979, 6195744825524974520506594, 12542605378501777687719638, 25387442211907212668978529, 51379347333621739925167237, 103967620486858109024891972, 210353092612945476399041696, 425541888504349469496747419, 860755183565615972390977335, 1740853180245066011577080182, 3520391986717800156744578138, 7118155225890936580670164965, 14391052956692545695702527001, 29091590923206436460129634552, 58802151866055563057708623492, 118842243771396506390316156095, 240160367621363773330430337963, 485272495399869067760456942410, 980448511114021177720106640286, 1980704062856608439838599021737, 4001022206970349048473969763949, 8081272576454962434541483215084, 16321001477938453544270054059048, 32958915605933964438914283638819
Generating function in Maple syntax:
(6*x^7-2*x^6-8*x^5+20*x^4-28*x^3+20*x^2-7*x+1)/(2*x-1)^2/(-1+x)^4
Generating function in latex syntax:
\frac{6 x^{7}-2 x^{6}-8 x^{5}+20 x^{4}-28 x^{3}+20 x^{2}-7 x +1}{\left(2 x -1\right)^{2} \left(-1+x \right)^{4}}
Generating function in sympy syntax:
(6*x**7 - 2*x**6 - 8*x**5 + 20*x**4 - 28*x**3 + 20*x**2 - 7*x + 1)/((x - 1)**4*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
-(2*x-1)^2*(-1+x)^4*F(x)+6*x^7-2*x^6-8*x^5+20*x^4-28*x^3+20*x^2-7*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right)^{2} \left(-1+x \right)^{4} F \! \left(x \right)+6 x^{7}-2 x^{6}-8 x^{5}+20 x^{4}-28 x^{3}+20 x^{2}-7 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,-7+1/3*n^3-7/2*n^2+43/6*n+1/4*2^n*n+2^n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ -7+\frac{n^{3}}{3}-\frac{7 n^{2}}{2}+\frac{43 n}{6}+\frac{2^{n} n}{4}+2^{n} & \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) = 142
a(7) = 338
a(n+2) = 1/3*n^3-11/2*n^2-4*a(n)+4*a(n+1)+127/6*n-20, n >= 8
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) = 142
a \! \left(7\right) = 338
a \! \left(n +2\right) = \frac{n^{3}}{3}-\frac{11 n^{2}}{2}-4 a \! \left(n \right)+4 a \! \left(n +1\right)+\frac{127 n}{6}-20, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18181/
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[19,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[13,x]
F[19,x] = F[20,x]+F[29,x]
F[20,x] = F[21,x]
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[23,x]+F[9,x]
F[23,x] = F[14,x]+F[24,x]
F[24,x] = F[25,x]+F[26,x]+F[28,x]
F[25,x] = 0
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[10,x]+F[24,x]
F[28,x] = F[12,x]*F[23,x]
F[29,x] = F[25,x]+F[30,x]+F[88,x]
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[32,x]+F[48,x]
F[32,x] = F[33,x]+F[6,x]
F[33,x] = F[25,x]+F[34,x]+F[37,x]
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[10,x]+F[36,x]
F[36,x] = F[34,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[39,x]+F[42,x]
F[39,x] = F[12,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[12,x]*F[39,x]
F[42,x] = F[43,x]+F[46,x]
F[43,x] = F[44,x]
F[44,x] = F[12,x]*F[45,x]
F[45,x] = F[12,x]+F[43,x]
F[46,x] = F[47,x]
F[47,x] = F[12,x]*F[42,x]
F[48,x] = F[49,x]+F[70,x]
F[49,x] = F[25,x]+F[50,x]+F[52,x]
F[50,x] = F[12,x]*F[51,x]
F[51,x] = F[49,x]+F[6,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[23,x]+F[54,x]
F[54,x] = F[55,x]+F[63,x]
F[55,x] = F[25,x]+F[56,x]+F[60,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[12,x]+F[58,x]
F[58,x] = F[25,x]+F[56,x]+F[59,x]
F[59,x] = F[12,x]*F[14,x]
F[60,x] = F[12,x]*F[61,x]
F[61,x] = F[14,x]+F[62,x]
F[62,x] = F[60,x]
F[63,x] = 2*F[25,x]+F[64,x]+F[69,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[40,x]+F[66,x]
F[66,x] = 2*F[25,x]+F[64,x]+F[67,x]
F[67,x] = F[12,x]*F[68,x]
F[68,x] = F[58,x]+F[66,x]
F[69,x] = F[12,x]*F[54,x]
F[70,x] = F[25,x]+F[71,x]+F[73,x]+F[78,x]
F[71,x] = F[12,x]*F[72,x]
F[72,x] = F[33,x]+F[70,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[24,x]+F[75,x]
F[75,x] = 2*F[25,x]+F[73,x]+F[76,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[36,x]+F[75,x]
F[78,x] = F[12,x]*F[79,x]
F[79,x] = F[68,x]+F[80,x]
F[80,x] = F[81,x]+F[86,x]
F[81,x] = F[82,x]
F[82,x] = F[12,x]*F[83,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[59,x]
F[85,x] = F[82,x]
F[86,x] = F[87,x]
F[87,x] = F[12,x]*F[80,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[101,x]+F[90,x]
F[90,x] = F[20,x]+F[91,x]
F[91,x] = F[100,x]+F[25,x]+F[92,x]
F[92,x] = F[12,x]*F[93,x]
F[93,x] = F[94,x]+F[96,x]
F[94,x] = F[10,x]+F[95,x]
F[95,x] = F[25,x]+F[34,x]+F[41,x]
F[96,x] = F[24,x]+F[97,x]
F[97,x] = F[25,x]+F[67,x]+F[73,x]+F[98,x]
F[98,x] = F[12,x]*F[99,x]
F[99,x] = F[95,x]+F[97,x]
F[100,x] = F[12,x]*F[90,x]
F[101,x] = F[102,x]+F[113,x]
F[102,x] = F[103,x]+F[25,x]+F[60,x]
F[103,x] = F[104,x]*F[12,x]
F[104,x] = F[105,x]+F[108,x]
F[105,x] = F[106,x]+F[12,x]
F[106,x] = F[107,x]
F[107,x] = F[105,x]*F[12,x]
F[108,x] = F[109,x]+F[58,x]
F[109,x] = 2*F[25,x]+F[110,x]+F[112,x]
F[110,x] = F[111,x]*F[12,x]
F[111,x] = F[106,x]+F[109,x]
F[112,x] = F[108,x]*F[12,x]
F[113,x] = 2*F[25,x]+F[114,x]+F[118,x]
F[114,x] = F[115,x]*F[12,x]
F[115,x] = F[116,x]+F[117,x]
F[116,x] = F[40,x]
F[117,x] = F[66,x]
F[118,x] = F[101,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_{19}\! \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_{13}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{29}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{9}\! \left(x \right)
F_{23}\! \left(x \right) = F_{14}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = 0
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{10}\! \left(x \right)+F_{24}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{29}\! \left(x \right) = F_{25}\! \left(x \right)+F_{30}\! \left(x \right)+F_{88}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{48}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{6}\! \left(x \right)
F_{33}\! \left(x \right) = F_{25}\! \left(x \right)+F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{10}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{34}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \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_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right)+F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{70}\! \left(x \right)
F_{49}\! \left(x \right) = F_{25}\! \left(x \right)+F_{50}\! \left(x \right)+F_{52}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{49}\! \left(x \right)+F_{6}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{23}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{63}\! \left(x \right)
F_{55}\! \left(x \right) = F_{25}\! \left(x \right)+F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{25}\! \left(x \right)+F_{56}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{14}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{64}\! \left(x \right)+F_{69}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{40}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{64}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{58}\! \left(x \right)+F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{70}\! \left(x \right) = F_{25}\! \left(x \right)+F_{71}\! \left(x \right)+F_{73}\! \left(x \right)+F_{78}\! \left(x \right)
F_{71}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{33}\! \left(x \right)+F_{70}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{24}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{73}\! \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_{36}\! \left(x \right)+F_{75}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{68}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{86}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{59}\! \left(x \right)
F_{85}\! \left(x \right) = F_{82}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{101}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{20}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{100}\! \left(x \right)+F_{25}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{96}\! \left(x \right)
F_{94}\! \left(x \right) = F_{10}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{25}\! \left(x \right)+F_{34}\! \left(x \right)+F_{41}\! \left(x \right)
F_{96}\! \left(x \right) = F_{24}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{25}\! \left(x \right)+F_{67}\! \left(x \right)+F_{73}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{95}\! \left(x \right)+F_{97}\! \left(x \right)
F_{100}\! \left(x \right) = F_{12}\! \left(x \right) F_{90}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{113}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{25}\! \left(x \right)+F_{60}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{12}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{108}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{12}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{105}\! \left(x \right) F_{12}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{58}\! \left(x \right)
F_{109}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{110}\! \left(x \right)+F_{112}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{12}\! \left(x \right)
F_{111}\! \left(x \right) = F_{106}\! \left(x \right)+F_{109}\! \left(x \right)
F_{112}\! \left(x \right) = F_{108}\! \left(x \right) F_{12}\! \left(x \right)
F_{113}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{114}\! \left(x \right)+F_{118}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{12}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{117}\! \left(x \right)
F_{116}\! \left(x \right) = F_{40}\! \left(x \right)
F_{117}\! \left(x \right) = F_{66}\! \left(x \right)
F_{118}\! \left(x \right) = F_{101}\! \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_19(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_13(x))
Eq(F_19(x), F_20(x) + F_29(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_12(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_9(x))
Eq(F_23(x), F_14(x) + F_24(x))
Eq(F_24(x), F_25(x) + F_26(x) + F_28(x))
Eq(F_25(x), 0)
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_10(x) + F_24(x))
Eq(F_28(x), F_12(x)*F_23(x))
Eq(F_29(x), F_25(x) + F_30(x) + F_88(x))
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_48(x))
Eq(F_32(x), F_33(x) + F_6(x))
Eq(F_33(x), F_25(x) + F_34(x) + F_37(x))
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_10(x) + F_36(x))
Eq(F_36(x), F_34(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_42(x))
Eq(F_39(x), F_12(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_12(x)*F_39(x))
Eq(F_42(x), F_43(x) + F_46(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_12(x)*F_45(x))
Eq(F_45(x), F_12(x) + F_43(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_12(x)*F_42(x))
Eq(F_48(x), F_49(x) + F_70(x))
Eq(F_49(x), F_25(x) + F_50(x) + F_52(x))
Eq(F_50(x), F_12(x)*F_51(x))
Eq(F_51(x), F_49(x) + F_6(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_23(x) + F_54(x))
Eq(F_54(x), F_55(x) + F_63(x))
Eq(F_55(x), F_25(x) + F_56(x) + F_60(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_12(x) + F_58(x))
Eq(F_58(x), F_25(x) + F_56(x) + F_59(x))
Eq(F_59(x), F_12(x)*F_14(x))
Eq(F_60(x), F_12(x)*F_61(x))
Eq(F_61(x), F_14(x) + F_62(x))
Eq(F_62(x), F_60(x))
Eq(F_63(x), 2*F_25(x) + F_64(x) + F_69(x))
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_40(x) + F_66(x))
Eq(F_66(x), 2*F_25(x) + F_64(x) + F_67(x))
Eq(F_67(x), F_12(x)*F_68(x))
Eq(F_68(x), F_58(x) + F_66(x))
Eq(F_69(x), F_12(x)*F_54(x))
Eq(F_70(x), F_25(x) + F_71(x) + F_73(x) + F_78(x))
Eq(F_71(x), F_12(x)*F_72(x))
Eq(F_72(x), F_33(x) + F_70(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_24(x) + F_75(x))
Eq(F_75(x), 2*F_25(x) + F_73(x) + F_76(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_36(x) + F_75(x))
Eq(F_78(x), F_12(x)*F_79(x))
Eq(F_79(x), F_68(x) + F_80(x))
Eq(F_80(x), F_81(x) + F_86(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_12(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_59(x))
Eq(F_85(x), F_82(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_12(x)*F_80(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_101(x) + F_90(x))
Eq(F_90(x), F_20(x) + F_91(x))
Eq(F_91(x), F_100(x) + F_25(x) + F_92(x))
Eq(F_92(x), F_12(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_96(x))
Eq(F_94(x), F_10(x) + F_95(x))
Eq(F_95(x), F_25(x) + F_34(x) + F_41(x))
Eq(F_96(x), F_24(x) + F_97(x))
Eq(F_97(x), F_25(x) + F_67(x) + F_73(x) + F_98(x))
Eq(F_98(x), F_12(x)*F_99(x))
Eq(F_99(x), F_95(x) + F_97(x))
Eq(F_100(x), F_12(x)*F_90(x))
Eq(F_101(x), F_102(x) + F_113(x))
Eq(F_102(x), F_103(x) + F_25(x) + F_60(x))
Eq(F_103(x), F_104(x)*F_12(x))
Eq(F_104(x), F_105(x) + F_108(x))
Eq(F_105(x), F_106(x) + F_12(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_105(x)*F_12(x))
Eq(F_108(x), F_109(x) + F_58(x))
Eq(F_109(x), F_110(x) + F_112(x) + 2*F_25(x))
Eq(F_110(x), F_111(x)*F_12(x))
Eq(F_111(x), F_106(x) + F_109(x))
Eq(F_112(x), F_108(x)*F_12(x))
Eq(F_113(x), F_114(x) + F_118(x) + 2*F_25(x))
Eq(F_114(x), F_115(x)*F_12(x))
Eq(F_115(x), F_116(x) + F_117(x))
Eq(F_116(x), F_40(x))
Eq(F_117(x), F_66(x))
Eq(F_118(x), F_101(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": [1, 3, 2, 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, 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": [1, 3, 2, 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, 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": [1, 3, 2, 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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"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": [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], [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": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 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": [[0, 1], [0, 1], [0, 1]]}, {"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": [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], [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": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 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]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"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": [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], [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": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"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": [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], [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": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 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]]}], 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