0123_0213_0321_1032_1320

Counting sequence:
1, 1, 2, 6, 19, 54, 149, 404, 1084, 2889, 7664, 20264, 53449, 140724, 370004, 971849, 2550664, 6690384, 17540969, 45973484, 120461404, 315574569, 826589984, 2164850744, 5669272969, 14845589604, 38872738724, 101783112329, 266497569784, 697751540064, 1826840936489, 4782939041564, 12522311732524, 32784667244649, 85833032178704, 224717113646024, 588323677468489, 1540264656177684, 4032491765901044, 10557253591198409, 27639354907040104, 72360982928613744, 189443937476184809, 495971516694708044, 1298471986997474044, 3399447193076783529, 8899875089791015424, 23300189071412540504, 61000714114679161609, 159701997253090055364, 418105365605521226564, 1094614275485334068489, 2865737812694201867224, 7502599866284713309824, 19642063193534821615529, 51423592529069518643324, 134628720023173268527564, 352462578799449355365609, 922759038893172934421744, 2415814582916065721604584, 6324684799927016777801929, 16558239997008969706621044, 43350035551387862531700884, 113491867377730558267760969, 297125568022955693030140744, 777884839573440282339778704, 2036528956461972677023430249, 5331702041341692794798981804, 13958577190621535799510454684, 36544029576639774788006261289, 95673511631531508933056087264, 250476505502422192748257516664, 655756005244669950785907495049, 1716791510969457422557847033124, 4494618529139441842784397733604, 11767064079400347157588874426249, 30806573714964557733569282062264, 80652657077299242250293084794784, 211151397540545001431658198390569, 552801535591559426873377962513884, 1447253209328580608845868593425004, 3788958092583077058979013626308969, 9919621068798439886720743902597584, 25969905114567821238442361315675144, 67990094276416181103124626512810569, 178000377717703036619968091159522004, 466011038882737557854852792839286324, 1220032738942598895140736579105398729, 3194087177969237643959649527971033384, 8362228795013471069522797171795948464, 21892599207167889630177912321393306089, 57315568826683625952149280460336957964, 150054107273269844488546610395523544124, 392846752993899620038043913398045627049, 1028486151709976440674691855142237242304, 2692611702139124552084245102715913910424, 7049348954713586915774470354380000110089, 18455435162014015595632019763173077662084, 48316956531353218671907296540637215360644, 126495434432095158021661285069734533388809, 331169346765031290596219389090558314743704

Generating function in Maple syntax:
-(x^7-3*x^6+4*x^5+3*x^3-8*x^2+5*x-1)/(x-1)/(2*x-1)/(x^2-3*x+1)

Generating function in latex syntax:
-\frac{x^{7}-3 x^{6}+4 x^{5}+3 x^{3}-8 x^{2}+5 x -1}{\left(x -1\right) \left(2 x -1\right) \left(x^{2}-3 x +1\right)}

Generating function in sympy syntax:
(-x**7 + 3*x**6 - 4*x**5 - 3*x**3 + 8*x**2 - 5*x + 1)/((x - 1)*(2*x - 1)*(x**2 - 3*x + 1))

Implicit equation for the generating function in Maple syntax:
(x-1)*(2*x-1)*(x^2-3*x+1)*F(x)+x^7-3*x^6+4*x^5+3*x^3-8*x^2+5*x-1 = 0

Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(2 x -1\right) \left(x^{2}-3 x +1\right) F \! \left(x \right)+x^{7}-3 x^{6}+4 x^{5}+3 x^{3}-8 x^{2}+5 x -1 = 0

Explicit closed form in Maple syntax:
-1/2*piecewise(n = 0,123/8,n = 1,19/4,n = 2,3/2,n = 3,1,0)-1+2*(3/2+1/2*5^(1/2))^(-n)*5^(1/2)-2*(3/2-1/2*5^(1/2))^(-n)*5^(1/2)+5*(3/2+1/2*5^(1/2))^(-n)-5/16*2^n+5*(3/2-1/2*5^(1/2))^(-n)

Explicit closed form in latex syntax:
-\frac{\left(\left\{\begin{array}{cc}\frac{123}{8} & n =0 \\ \frac{19}{4} & n =1 \\ \frac{3}{2} & n =2 \\ 1 & n =3 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)}{2}-1+2 \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}-2 \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}+5 \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}-\frac{5 \,2^{n}}{16}+5 \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 54
a(6) = 149
a(7) = 404
a(n+3) = 2*a(n)-7*a(n+1)+5*a(n+2)-1, 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) = 54
a \! \left(6\right) = 149
a \! \left(7\right) = 404
a \! \left(n +3\right) = 2 a \! \left(n \right)-7 a \! \left(n +1\right)+5 a \! \left(n +2\right)-1, \quad n \geq 8

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16821/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[20,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[4,x]
F[14,x] = F[15,x]+F[17,x]
F[15,x] = F[16,x]
F[16,x] = F[13,x]*F[4,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[15,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[114,x]+F[22,x]+F[23,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[37,x]
F[25,x] = F[15,x]+F[26,x]
F[26,x] = F[22,x]+F[27,x]+F[35,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[30,x]+F[4,x]
F[30,x] = F[31,x]
F[31,x] = x^2
F[32,x] = F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[15,x]*F[4,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[15,x]+F[33,x]
F[37,x] = F[104,x]+F[38,x]
F[38,x] = F[22,x]+F[23,x]+F[39,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[2,x]+F[41,x]
F[41,x] = F[103,x]+F[22,x]+F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[46,x]
F[44,x] = F[4,x]+F[45,x]
F[45,x] = F[22,x]+F[27,x]+F[34,x]
F[46,x] = F[41,x]+F[47,x]
F[47,x] = F[22,x]+F[48,x]+F[65,x]+F[97,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[57,x]
F[50,x] = F[51,x]+F[54,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[4,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[33,x]
F[57,x] = F[58,x]+F[61,x]
F[58,x] = 2*F[22,x]+F[48,x]+F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[41,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[73,x]
F[69,x] = F[15,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[4,x]
F[73,x] = F[66,x]+F[74,x]
F[74,x] = 2*F[22,x]+F[75,x]+F[95,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[77,x]+F[79,x]
F[77,x] = F[78,x]
F[78,x] = F[52,x]
F[79,x] = F[80,x]
F[80,x] = 2*F[22,x]+F[75,x]+F[81,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[86,x]+F[88,x]
F[86,x] = F[4,x]+F[87,x]
F[87,x] = F[71,x]
F[88,x] = F[83,x]+F[89,x]
F[89,x] = 2*F[22,x]+F[90,x]+F[95,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[92,x]+F[93,x]
F[92,x] = F[51,x]
F[93,x] = F[94,x]
F[94,x] = 2*F[22,x]+F[81,x]+F[90,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[83,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[102,x]+F[99,x]
F[99,x] = F[100,x]+F[41,x]
F[100,x] = F[101,x]
F[101,x] = F[4,x]*F[83,x]
F[102,x] = F[64,x]
F[103,x] = F[2,x]*F[4,x]
F[104,x] = F[105,x]+F[112,x]+F[22,x]+F[97,x]
F[105,x] = F[106,x]*F[4,x]
F[106,x] = F[107,x]+F[109,x]
F[107,x] = F[108,x]+F[78,x]
F[108,x] = F[55,x]
F[109,x] = F[110,x]+F[111,x]
F[110,x] = 2*F[22,x]+F[105,x]+F[59,x]
F[111,x] = F[62,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[64,x]+F[66,x]
F[114,x] = F[115,x]*F[4,x]
F[115,x] = F[116,x]+F[120,x]
F[116,x] = F[117,x]+F[2,x]
F[117,x] = F[118,x]+F[22,x]+F[42,x]
F[118,x] = F[119,x]*F[4,x]
F[119,x] = F[2,x]+F[83,x]
F[120,x] = F[121,x]+F[66,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x]*F[4,x]
F[123,x] = F[66,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{20}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{15}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{114}\! \left(x \right)+F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{37}\! \left(x \right)
F_{25}\! \left(x \right) = F_{15}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{35}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = x^{2}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{15}\! \left(x \right)+F_{33}\! \left(x \right)
F_{37}\! \left(x \right) = F_{104}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{103}\! \left(x \right)+F_{22}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{46}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{34}\! \left(x \right)
F_{46}\! \left(x \right) = F_{41}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{22}\! \left(x \right)+F_{48}\! \left(x \right)+F_{65}\! \left(x \right)+F_{97}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{57}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{54}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{33}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{48}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{41}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{73}\! \left(x \right)
F_{69}\! \left(x \right) = F_{15}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right)
F_{73}\! \left(x \right) = F_{66}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{75}\! \left(x \right)+F_{95}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{79}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{52}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{75}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{88}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{71}\! \left(x \right)
F_{88}\! \left(x \right) = F_{83}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{90}\! \left(x \right)+F_{95}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{93}\! \left(x \right)
F_{92}\! \left(x \right) = F_{51}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{81}\! \left(x \right)+F_{90}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{83}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{102}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{41}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{102}\! \left(x \right) = F_{64}\! \left(x \right)
F_{103}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{112}\! \left(x \right)+F_{22}\! \left(x \right)+F_{97}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{109}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{78}\! \left(x \right)
F_{108}\! \left(x \right) = F_{55}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{111}\! \left(x \right)
F_{110}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{105}\! \left(x \right)+F_{59}\! \left(x \right)
F_{111}\! \left(x \right) = F_{62}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{64}\! \left(x \right)+F_{66}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{4}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{120}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{2}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{22}\! \left(x \right)+F_{42}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{2}\! \left(x \right)+F_{83}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{66}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{4}\! \left(x \right)
F_{123}\! \left(x \right) = F_{66}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_20(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_4(x))
Eq(F_14(x), F_15(x) + F_17(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_13(x)*F_4(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_15(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_114(x) + F_22(x) + F_23(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_37(x))
Eq(F_25(x), F_15(x) + F_26(x))
Eq(F_26(x), F_22(x) + F_27(x) + F_35(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_30(x) + F_4(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), x**2)
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_15(x)*F_4(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_15(x) + F_33(x))
Eq(F_37(x), F_104(x) + F_38(x))
Eq(F_38(x), F_22(x) + F_23(x) + F_39(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_2(x) + F_41(x))
Eq(F_41(x), F_103(x) + F_22(x) + F_42(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_46(x))
Eq(F_44(x), F_4(x) + F_45(x))
Eq(F_45(x), F_22(x) + F_27(x) + F_34(x))
Eq(F_46(x), F_41(x) + F_47(x))
Eq(F_47(x), F_22(x) + F_48(x) + F_65(x) + F_97(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_57(x))
Eq(F_50(x), F_51(x) + F_54(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_4(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_33(x))
Eq(F_57(x), F_58(x) + F_61(x))
Eq(F_58(x), 2*F_22(x) + F_48(x) + F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_41(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_73(x))
Eq(F_69(x), F_15(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_4(x))
Eq(F_73(x), F_66(x) + F_74(x))
Eq(F_74(x), 2*F_22(x) + F_75(x) + F_95(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_79(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_52(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), 2*F_22(x) + F_75(x) + F_81(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_88(x))
Eq(F_86(x), F_4(x) + F_87(x))
Eq(F_87(x), F_71(x))
Eq(F_88(x), F_83(x) + F_89(x))
Eq(F_89(x), 2*F_22(x) + F_90(x) + F_95(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_93(x))
Eq(F_92(x), F_51(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), 2*F_22(x) + F_81(x) + F_90(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(x), F_83(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_102(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_41(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_4(x)*F_83(x))
Eq(F_102(x), F_64(x))
Eq(F_103(x), F_2(x)*F_4(x))
Eq(F_104(x), F_105(x) + F_112(x) + F_22(x) + F_97(x))
Eq(F_105(x), F_106(x)*F_4(x))
Eq(F_106(x), F_107(x) + F_109(x))
Eq(F_107(x), F_108(x) + F_78(x))
Eq(F_108(x), F_55(x))
Eq(F_109(x), F_110(x) + F_111(x))
Eq(F_110(x), F_105(x) + 2*F_22(x) + F_59(x))
Eq(F_111(x), F_62(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_64(x) + F_66(x))
Eq(F_114(x), F_115(x)*F_4(x))
Eq(F_115(x), F_116(x) + F_120(x))
Eq(F_116(x), F_117(x) + F_2(x))
Eq(F_117(x), F_118(x) + F_22(x) + F_42(x))
Eq(F_118(x), F_119(x)*F_4(x))
Eq(F_119(x), F_2(x) + F_83(x))
Eq(F_120(x), F_121(x) + F_66(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x)*F_4(x))
Eq(F_123(x), F_66(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, 2, 3], "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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 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, 2, 3], "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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 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, 2, 3], "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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 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], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"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], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"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], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 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