0132_1032_2310
Counting sequence:
1, 1, 2, 6, 21, 73, 239, 734, 2134, 5934, 15918, 41470, 105470, 262910, 644350, 1556478, 3713022, 8761342, 20475902, 47448062, 109117438, 249233406, 565772286, 1277165566, 2868379646, 6412042238, 14272167934, 31641829374, 69893881854, 153863847934, 337641471998, 738734374910, 1611820695550, 3507646103550, 7614708580350, 16492674416638, 35643933589502, 76875619631102, 165480794947582, 355554572632062, 762614393077758, 1632980925677566, 3491155576619006, 7452489813065726, 15885743998107646, 33815480112250878, 71887169735622654, 152629806121353214, 323669834938187774, 685585082336935934, 1450563700292321278, 3065825446332465150, 6473080039414956030, 13653506695303790590, 28771527694433124350, 60573414988133171198, 127413588857752387582, 267779530243822321662, 562314945873852760062, 1179871044777032024062, 2473737203322066042878, 5182598335989890940926, 10849928107072923107326, 22698718582699603263486, 47454825590370124955646, 99145484788665805701118, 207008209073663981387774, 431948959229982860640254, 900772959863311114960894, 1877343591125494777511934, 3910433042465319299317758, 8140769520656909642760190, 16938390704290468999462910, 35225017039440221707436030, 73216455394126517451620350, 152107424413231272333148158, 315850759840253350472843262, 655554192785481278920065022, 1359989601035146255447097342, 2820121705706026207295832062, 5845345232496046845512908798, 12110641071580725500589375486, 25080903958771178258718261246, 51920946100809093795280846846, 107440864366610938643661979646, 222242878048855354332109864958, 459538091477732456518486327294, 949848180767935684049943658494, 1962589518375502836284801417214, 4053692687079319212357568167934, 8369925376552708213327727165438, 17276072218247124426354728108030, 35647102401242167705857731592190, 73529615028423910843114556751870, 151621967556643912034438560612350, 312555101118772811806530884075518, 644107630080419069311663728492542, 1326967735150627682748769641693182, 2732970514169391183768198970343422, 5627101014413110313243865528664062, 11582761218772874834488157819371518
Generating function in Maple syntax:
(x^7+2*x^6+4*x^5-23*x^4+36*x^3-25*x^2+8*x-1)/(x-1)/(2*x-1)^4
Generating function in latex syntax:
\frac{x^{7}+2 x^{6}+4 x^{5}-23 x^{4}+36 x^{3}-25 x^{2}+8 x -1}{\left(x -1\right) \left(2 x -1\right)^{4}}
Generating function in sympy syntax:
(x**7 + 2*x**6 + 4*x**5 - 23*x**4 + 36*x**3 - 25*x**2 + 8*x - 1)/((x - 1)*(2*x - 1)**4)
Implicit equation for the generating function in Maple syntax:
-(x-1)*(2*x-1)^4*F(x)+x^7+2*x^6+4*x^5-23*x^4+36*x^3-25*x^2+8*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x -1\right) \left(2 x -1\right)^{4} F \! \left(x \right)+x^{7}+2 x^{6}+4 x^{5}-23 x^{4}+36 x^{3}-25 x^{2}+8 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,-2+1/128*(n^3+18*n^2-107*n+260)*2^n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ -2+\frac{\left(n^{3}+18 n^{2}-107 n +260\right) 2^{n}}{128} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 73
a(6) = 239
a(7) = 734
a(n+4) = -16*a(n)+32*a(n+1)-24*a(n+2)+8*a(n+3)-2, 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) = 21
a \! \left(5\right) = 73
a \! \left(6\right) = 239
a \! \left(7\right) = 734
a \! \left(n +4\right) = -16 a \! \left(n \right)+32 a \! \left(n +1\right)-24 a \! \left(n +2\right)+8 a \! \left(n +3\right)-2, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14713/
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[38,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[26,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[9,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[19,x]
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[1,x]+F[18,x]
F[21,x] = F[22,x]+F[23,x]+F[25,x]
F[22,x] = 0
F[23,x] = F[12,x]*F[24,x]
F[24,x] = F[10,x]+F[21,x]
F[25,x] = F[12,x]*F[17,x]
F[26,x] = F[22,x]+F[27,x]+F[37,x]
F[27,x] = F[12,x]*F[28,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[10,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[12,x]*F[29,x]
F[32,x] = F[21,x]+F[33,x]
F[33,x] = 2*F[22,x]+F[34,x]+F[36,x]
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[30,x]+F[33,x]
F[36,x] = F[12,x]*F[32,x]
F[37,x] = F[12,x]*F[13,x]
F[38,x] = F[39,x]+F[55,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[1,x]+F[14,x]
F[43,x] = F[18,x]+F[44,x]
F[44,x] = F[22,x]+F[23,x]+F[45,x]
F[45,x] = F[12,x]*F[46,x]
F[46,x] = F[17,x]+F[47,x]
F[47,x] = F[48,x]+F[51,x]
F[48,x] = F[49,x]
F[49,x] = F[12,x]*F[50,x]
F[50,x] = F[18,x]+F[48,x]
F[51,x] = 2*F[22,x]+F[52,x]+F[54,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[21,x]+F[51,x]
F[54,x] = F[12,x]*F[47,x]
F[55,x] = F[22,x]+F[56,x]+F[70,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[10,x]+F[26,x]
F[59,x] = F[21,x]+F[60,x]
F[60,x] = F[22,x]+F[34,x]+F[61,x]+F[68,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[32,x]+F[63,x]
F[63,x] = F[51,x]+F[64,x]
F[64,x] = 3*F[22,x]+F[65,x]+F[67,x]
F[65,x] = F[12,x]*F[66,x]
F[66,x] = F[33,x]+F[64,x]
F[67,x] = F[12,x]*F[63,x]
F[68,x] = F[12,x]*F[69,x]
F[69,x] = F[44,x]+F[60,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[72,x]+F[75,x]
F[72,x] = F[39,x]+F[73,x]
F[73,x] = F[22,x]+F[56,x]+F[74,x]
F[74,x] = F[12,x]*F[72,x]
F[75,x] = F[76,x]+F[83,x]
F[76,x] = F[22,x]+F[45,x]+F[77,x]
F[77,x] = F[12,x]*F[78,x]
F[78,x] = F[79,x]+F[81,x]
F[79,x] = F[10,x]+F[80,x]
F[80,x] = F[22,x]+F[25,x]+F[27,x]
F[81,x] = F[21,x]+F[82,x]
F[82,x] = F[22,x]+F[34,x]+F[54,x]+F[61,x]
F[83,x] = F[107,x]+F[22,x]+F[61,x]+F[84,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[86,x]+F[98,x]
F[86,x] = F[30,x]+F[87,x]
F[87,x] = 2*F[22,x]+F[36,x]+F[88,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[90,x]+F[93,x]
F[90,x] = F[30,x]+F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[12,x]*F[90,x]
F[93,x] = F[33,x]+F[94,x]
F[94,x] = 3*F[22,x]+F[95,x]+F[97,x]
F[95,x] = F[12,x]*F[96,x]
F[96,x] = F[91,x]+F[94,x]
F[97,x] = F[12,x]*F[93,x]
F[98,x] = F[33,x]+F[99,x]
F[99,x] = 2*F[22,x]+F[100,x]+F[67,x]+F[95,x]
F[100,x] = F[101,x]*F[12,x]
F[101,x] = F[102,x]+F[93,x]
F[102,x] = F[103,x]+F[64,x]
F[103,x] = 4*F[22,x]+F[104,x]+F[106,x]
F[104,x] = F[105,x]*F[12,x]
F[105,x] = F[103,x]+F[94,x]
F[106,x] = F[102,x]*F[12,x]
F[107,x] = F[12,x]*F[75,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_{38}\! \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_{26}\! \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_{17}\! \left(x \right)+F_{9}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \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_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{10}\! \left(x \right)+F_{21}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{26}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{37}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = F_{10}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{21}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{34}\! \left(x \right)+F_{36}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{30}\! \left(x \right)+F_{33}\! \left(x \right)
F_{36}\! \left(x \right) = F_{12}\! \left(x \right) F_{32}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{55}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{43}\! \left(x \right) = F_{18}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{17}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{18}\! \left(x \right)+F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = 2 F_{22}\! \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_{21}\! \left(x \right)+F_{51}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{55}\! \left(x \right) = F_{22}\! \left(x \right)+F_{56}\! \left(x \right)+F_{70}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{10}\! \left(x \right)+F_{26}\! \left(x \right)
F_{59}\! \left(x \right) = F_{21}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{22}\! \left(x \right)+F_{34}\! \left(x \right)+F_{61}\! \left(x \right)+F_{68}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{32}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{51}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{33}\! \left(x \right)+F_{64}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{44}\! \left(x \right)+F_{60}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{75}\! \left(x \right)
F_{72}\! \left(x \right) = F_{39}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{22}\! \left(x \right)+F_{56}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{83}\! \left(x \right)
F_{76}\! \left(x \right) = F_{22}\! \left(x \right)+F_{45}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{81}\! \left(x \right)
F_{79}\! \left(x \right) = F_{10}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{22}\! \left(x \right)+F_{25}\! \left(x \right)+F_{27}\! \left(x \right)
F_{81}\! \left(x \right) = F_{21}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{22}\! \left(x \right)+F_{34}\! \left(x \right)+F_{54}\! \left(x \right)+F_{61}\! \left(x \right)
F_{83}\! \left(x \right) = F_{107}\! \left(x \right)+F_{22}\! \left(x \right)+F_{61}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{98}\! \left(x \right)
F_{86}\! \left(x \right) = F_{30}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{36}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{93}\! \left(x \right)
F_{90}\! \left(x \right) = F_{30}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{90}\! \left(x \right)
F_{93}\! \left(x \right) = F_{33}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{95}\! \left(x \right)+F_{97}\! \left(x \right)
F_{95}\! \left(x \right) = F_{12}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{91}\! \left(x \right)+F_{94}\! \left(x \right)
F_{97}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
F_{98}\! \left(x \right) = F_{33}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{100}\! \left(x \right)+F_{67}\! \left(x \right)+F_{95}\! \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_{93}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{64}\! \left(x \right)
F_{103}\! \left(x \right) = 4 F_{22}\! \left(x \right)+F_{104}\! \left(x \right)+F_{106}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{12}\! \left(x \right)
F_{105}\! \left(x \right) = F_{103}\! \left(x \right)+F_{94}\! \left(x \right)
F_{106}\! \left(x \right) = F_{102}\! \left(x \right) F_{12}\! \left(x \right)
F_{107}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \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_38(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_26(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_9(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_1(x) + F_18(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_25(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_12(x)*F_24(x))
Eq(F_24(x), F_10(x) + F_21(x))
Eq(F_25(x), F_12(x)*F_17(x))
Eq(F_26(x), F_22(x) + F_27(x) + F_37(x))
Eq(F_27(x), F_12(x)*F_28(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_10(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_12(x)*F_29(x))
Eq(F_32(x), F_21(x) + F_33(x))
Eq(F_33(x), 2*F_22(x) + F_34(x) + F_36(x))
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_30(x) + F_33(x))
Eq(F_36(x), F_12(x)*F_32(x))
Eq(F_37(x), F_12(x)*F_13(x))
Eq(F_38(x), F_39(x) + F_55(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_1(x) + F_14(x))
Eq(F_43(x), F_18(x) + F_44(x))
Eq(F_44(x), F_22(x) + F_23(x) + F_45(x))
Eq(F_45(x), F_12(x)*F_46(x))
Eq(F_46(x), F_17(x) + F_47(x))
Eq(F_47(x), F_48(x) + F_51(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_12(x)*F_50(x))
Eq(F_50(x), F_18(x) + F_48(x))
Eq(F_51(x), 2*F_22(x) + F_52(x) + F_54(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_21(x) + F_51(x))
Eq(F_54(x), F_12(x)*F_47(x))
Eq(F_55(x), F_22(x) + F_56(x) + F_70(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_10(x) + F_26(x))
Eq(F_59(x), F_21(x) + F_60(x))
Eq(F_60(x), F_22(x) + F_34(x) + F_61(x) + F_68(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_32(x) + F_63(x))
Eq(F_63(x), F_51(x) + F_64(x))
Eq(F_64(x), 3*F_22(x) + F_65(x) + F_67(x))
Eq(F_65(x), F_12(x)*F_66(x))
Eq(F_66(x), F_33(x) + F_64(x))
Eq(F_67(x), F_12(x)*F_63(x))
Eq(F_68(x), F_12(x)*F_69(x))
Eq(F_69(x), F_44(x) + F_60(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_75(x))
Eq(F_72(x), F_39(x) + F_73(x))
Eq(F_73(x), F_22(x) + F_56(x) + F_74(x))
Eq(F_74(x), F_12(x)*F_72(x))
Eq(F_75(x), F_76(x) + F_83(x))
Eq(F_76(x), F_22(x) + F_45(x) + F_77(x))
Eq(F_77(x), F_12(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_81(x))
Eq(F_79(x), F_10(x) + F_80(x))
Eq(F_80(x), F_22(x) + F_25(x) + F_27(x))
Eq(F_81(x), F_21(x) + F_82(x))
Eq(F_82(x), F_22(x) + F_34(x) + F_54(x) + F_61(x))
Eq(F_83(x), F_107(x) + F_22(x) + F_61(x) + F_84(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_98(x))
Eq(F_86(x), F_30(x) + F_87(x))
Eq(F_87(x), 2*F_22(x) + F_36(x) + F_88(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_93(x))
Eq(F_90(x), F_30(x) + F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_12(x)*F_90(x))
Eq(F_93(x), F_33(x) + F_94(x))
Eq(F_94(x), 3*F_22(x) + F_95(x) + F_97(x))
Eq(F_95(x), F_12(x)*F_96(x))
Eq(F_96(x), F_91(x) + F_94(x))
Eq(F_97(x), F_12(x)*F_93(x))
Eq(F_98(x), F_33(x) + F_99(x))
Eq(F_99(x), F_100(x) + 2*F_22(x) + F_67(x) + F_95(x))
Eq(F_100(x), F_101(x)*F_12(x))
Eq(F_101(x), F_102(x) + F_93(x))
Eq(F_102(x), F_103(x) + F_64(x))
Eq(F_103(x), F_104(x) + F_106(x) + 4*F_22(x))
Eq(F_104(x), F_105(x)*F_12(x))
Eq(F_105(x), F_103(x) + F_94(x))
Eq(F_106(x), F_102(x)*F_12(x))
Eq(F_107(x), F_12(x)*F_75(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": [1, 0, 3, 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": [1, 0, 3, 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": [1, 0, 3, 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": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 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": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 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]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 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": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 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]]}, {"patt": [2, 3, 1, 0], "pos": [[2, 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": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 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": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 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]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 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], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 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": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 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]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 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": [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, 2, 1], "pos": [[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": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 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": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 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]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 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, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 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": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 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]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], 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