0132_0213_0321_1203_1230

Counting sequence:
1, 1, 2, 6, 19, 57, 165, 467, 1301, 3581, 9763, 26413, 71013, 189955, 506021, 1343469, 3557155, 9397629, 24783189, 65263235, 171661877, 451098653, 1184517667, 3108483661, 8153516229, 21378279427, 56035848005, 146842510797, 384726565411, 1007823724701, 2639751241653, 6913510375043, 18105074850773, 47410572547325, 124144896402211, 325061697623149, 851117505878565, 2228449733802499, 5834558113043429, 15275894620225965, 39994500137169187, 104710423289827773, 274142542168359957, 717729022965250691, 1879068715983203189, 4919526603007608797, 12879612248109378595, 33719516849506548877, 88279360512875334021, 231119426706235629571, 605080678824435996293, 1584126198573025420173, 4147305235244034741283, 10857804425332844468445, 28426138440051983414901, 74420672819317982120579, 194836006118691529320725, 510087602241935365959869, 1335427323024671343536419, 3496195429681590724086445, 9153161127747921966560997, 23963292349075411489200643, 62736724854619973204104997, 164246900373298205680954221, 430004013158762791257860899, 1125765214042887967537681917, 2947291781155539719458985685, 7716110438406694425474264707, 20201040161253842063088563381, 52887011318180172849750486941, 138459996375830846805500123683, 362492983048187684500262543053, 949018963394056793151989236293, 2484563928679779773048461453315, 6504672866327172492537613350341, 17029454758846109258370226354509, 44583691589661081631619583833635, 116721620373759354817451206600989, 305581170268306154148398689305909, 800021891923426916214552748844675, 2094484508524289143531832493993557, 5483431639769627476180004930086013, 14355810423176082936058131337002787, 37583999654843832088997944456075501, 98396188592130297754750127368883109, 257604566224305755842495917500598787, 674417510288722210746453843182375525, 1765647965062567061622756564844277037, 4622526385750062751130514790343603491, 12101931193909131558900019750968128061, 31683267199459038286059676485714567573, 82947870411508767272714610019664343683, 217160344049303573983866026734618392053, 568533161765184060592268561575595470685, 1488439141304431789639352530912426858531, 3896784262265715612057900157277101906189, 10201913645730399534077140953699510711045, 26708956675405803725416250250482290425859, 69924956381457556632971347933268273958149, 183065912470927763195725835904762744219405, 479272781035287141079919376660697156216867

Generating function in Maple syntax:
-(3*x^6-x^5+6*x^4-19*x^3+18*x^2-7*x+1)/(-1+x)/(x^2-3*x+1)/(2*x-1)^2

Generating function in latex syntax:
-\frac{3 x^{6}-x^{5}+6 x^{4}-19 x^{3}+18 x^{2}-7 x +1}{\left(-1+x \right) \left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2}}

Generating function in sympy syntax:
(-3*x**6 + x**5 - 6*x**4 + 19*x**3 - 18*x**2 + 7*x - 1)/((x - 1)*(2*x - 1)**2*(x**2 - 3*x + 1))

Implicit equation for the generating function in Maple syntax:
(-1+x)*(x^2-3*x+1)*(2*x-1)^2*F(x)+3*x^6-x^5+6*x^4-19*x^3+18*x^2-7*x+1 = 0

Implicit equation for the generating function in latex syntax:
\left(-1+x \right) \left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} F \! \left(x \right)+3 x^{6}-x^{5}+6 x^{4}-19 x^{3}+18 x^{2}-7 x +1 = 0

Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/8*(-8*5^(1/2)+24)*(3/2-1/2*5^(1/2))^(-n)+1/8*(8*5^(1/2)+24)*(3/2+1/2*5^(1/2))^(-n)-1/8*2^n*n-2^(-1+n)-1)

Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{\left(-8 \sqrt{5}+24\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{8}+\frac{\left(8 \sqrt{5}+24\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{8}-\frac{2^{n} n}{8}-2^{-1+n}\\-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) = 57
a(6) = 165
a(n+4) = -4*a(n)+16*a(n+1)-17*a(n+2)+7*a(n+3)+1, n >= 7

Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 57
a \! \left(6\right) = 165
a \! \left(n +4\right) = -4 a \! \left(n \right)+16 a \! \left(n +1\right)-17 a \! \left(n +2\right)+7 a \! \left(n +3\right)+1, \quad n \geq 7

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18245/
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[12,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[13,x]
F[19,x] = F[20,x]+F[59,x]
F[20,x] = F[21,x]
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[12,x]*F[16,x]
F[26,x] = F[20,x]+F[27,x]
F[27,x] = F[28,x]+F[29,x]+F[57,x]
F[28,x] = 0
F[29,x] = F[12,x]*F[30,x]
F[30,x] = F[31,x]+F[35,x]
F[31,x] = F[24,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[12,x]
F[35,x] = F[27,x]+F[36,x]
F[36,x] = 2*F[28,x]+F[37,x]+F[41,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[32,x]
F[40,x] = F[36,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[28,x]+F[44,x]+F[56,x]
F[44,x] = F[12,x]*F[45,x]
F[45,x] = F[46,x]+F[49,x]
F[46,x] = F[12,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = x^2
F[49,x] = F[43,x]+F[50,x]
F[50,x] = 2*F[28,x]+F[51,x]+F[55,x]
F[51,x] = F[12,x]*F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = F[47,x]
F[54,x] = F[50,x]
F[55,x] = F[12,x]*F[43,x]
F[56,x] = F[12,x]*F[20,x]
F[57,x] = F[12,x]*F[58,x]
F[58,x] = F[20,x]+F[43,x]
F[59,x] = F[28,x]+F[60,x]+F[84,x]
F[60,x] = F[12,x]*F[61,x]
F[61,x] = F[62,x]+F[69,x]
F[62,x] = F[6,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[12,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[12,x]*F[66,x]
F[69,x] = F[59,x]+F[70,x]
F[70,x] = 2*F[28,x]+F[71,x]+F[75,x]
F[71,x] = F[12,x]*F[72,x]
F[72,x] = F[73,x]+F[74,x]
F[73,x] = F[63,x]
F[74,x] = F[70,x]
F[75,x] = F[12,x]*F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[43,x]+F[78,x]
F[78,x] = 2*F[28,x]+F[79,x]+F[83,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[81,x]+F[82,x]
F[81,x] = F[67,x]
F[82,x] = F[78,x]
F[83,x] = F[12,x]*F[77,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[86,x]+F[99,x]
F[86,x] = F[20,x]+F[87,x]
F[87,x] = F[28,x]+F[88,x]+F[98,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[90,x]+F[92,x]
F[90,x] = F[10,x]+F[91,x]
F[91,x] = F[68,x]
F[92,x] = F[87,x]+F[93,x]
F[93,x] = 2*F[28,x]+F[83,x]+F[94,x]
F[94,x] = F[12,x]*F[95,x]
F[95,x] = F[96,x]+F[97,x]
F[96,x] = F[91,x]
F[97,x] = F[93,x]
F[98,x] = F[12,x]*F[86,x]
F[99,x] = F[100,x]+F[102,x]
F[100,x] = F[101,x]+F[28,x]+F[44,x]
F[101,x] = F[12,x]*F[58,x]
F[102,x] = 2*F[28,x]+F[103,x]+F[79,x]
F[103,x] = F[12,x]*F[99,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_{12}\! \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_{59}\! \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_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{26}\! \left(x \right) = F_{20}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)+F_{57}\! \left(x \right)
F_{28}\! \left(x \right) = 0
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{31}\! \left(x \right) = F_{24}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right)
F_{35}\! \left(x \right) = F_{27}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{37}\! \left(x \right)+F_{41}\! \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_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{32}\! \left(x \right)
F_{40}\! \left(x \right) = F_{36}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{28}\! \left(x \right)+F_{44}\! \left(x \right)+F_{56}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{49}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = x^{2}
F_{49}\! \left(x \right) = F_{43}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{51}\! \left(x \right)+F_{55}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{47}\! \left(x \right)
F_{54}\! \left(x \right) = F_{50}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{20}\! \left(x \right)+F_{43}\! \left(x \right)
F_{59}\! \left(x \right) = F_{28}\! \left(x \right)+F_{60}\! \left(x \right)+F_{84}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{69}\! \left(x \right)
F_{62}\! \left(x \right) = F_{6}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{59}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{71}\! \left(x \right)+F_{75}\! \left(x \right)
F_{71}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = F_{63}\! \left(x \right)
F_{74}\! \left(x \right) = F_{70}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{43}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{79}\! \left(x \right)+F_{83}\! \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_{82}\! \left(x \right)
F_{81}\! \left(x \right) = F_{67}\! \left(x \right)
F_{82}\! \left(x \right) = F_{78}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \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_{99}\! \left(x \right)
F_{86}\! \left(x \right) = F_{20}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{28}\! \left(x \right)+F_{88}\! \left(x \right)+F_{98}\! \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_{92}\! \left(x \right)
F_{90}\! \left(x \right) = F_{10}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{68}\! \left(x \right)
F_{92}\! \left(x \right) = F_{87}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{83}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{97}\! \left(x \right)
F_{96}\! \left(x \right) = F_{91}\! \left(x \right)
F_{97}\! \left(x \right) = F_{93}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{86}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{102}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{28}\! \left(x \right)+F_{44}\! \left(x \right)
F_{101}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{102}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{103}\! \left(x \right)+F_{79}\! \left(x \right)
F_{103}\! \left(x \right) = F_{12}\! \left(x \right) F_{99}\! \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_12(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_59(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_26(x))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_12(x)*F_16(x))
Eq(F_26(x), F_20(x) + F_27(x))
Eq(F_27(x), F_28(x) + F_29(x) + F_57(x))
Eq(F_28(x), 0)
Eq(F_29(x), F_12(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_35(x))
Eq(F_31(x), F_24(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_12(x))
Eq(F_35(x), F_27(x) + F_36(x))
Eq(F_36(x), 2*F_28(x) + F_37(x) + F_41(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_40(x))
Eq(F_39(x), F_32(x))
Eq(F_40(x), F_36(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_28(x) + F_44(x) + F_56(x))
Eq(F_44(x), F_12(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_49(x))
Eq(F_46(x), F_12(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), x**2)
Eq(F_49(x), F_43(x) + F_50(x))
Eq(F_50(x), 2*F_28(x) + F_51(x) + F_55(x))
Eq(F_51(x), F_12(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), F_47(x))
Eq(F_54(x), F_50(x))
Eq(F_55(x), F_12(x)*F_43(x))
Eq(F_56(x), F_12(x)*F_20(x))
Eq(F_57(x), F_12(x)*F_58(x))
Eq(F_58(x), F_20(x) + F_43(x))
Eq(F_59(x), F_28(x) + F_60(x) + F_84(x))
Eq(F_60(x), F_12(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_69(x))
Eq(F_62(x), F_6(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_12(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_12(x)*F_66(x))
Eq(F_69(x), F_59(x) + F_70(x))
Eq(F_70(x), 2*F_28(x) + F_71(x) + F_75(x))
Eq(F_71(x), F_12(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_74(x))
Eq(F_73(x), F_63(x))
Eq(F_74(x), F_70(x))
Eq(F_75(x), F_12(x)*F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_43(x) + F_78(x))
Eq(F_78(x), 2*F_28(x) + F_79(x) + F_83(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_82(x))
Eq(F_81(x), F_67(x))
Eq(F_82(x), F_78(x))
Eq(F_83(x), F_12(x)*F_77(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_99(x))
Eq(F_86(x), F_20(x) + F_87(x))
Eq(F_87(x), F_28(x) + F_88(x) + F_98(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_92(x))
Eq(F_90(x), F_10(x) + F_91(x))
Eq(F_91(x), F_68(x))
Eq(F_92(x), F_87(x) + F_93(x))
Eq(F_93(x), 2*F_28(x) + F_83(x) + F_94(x))
Eq(F_94(x), F_12(x)*F_95(x))
Eq(F_95(x), F_96(x) + F_97(x))
Eq(F_96(x), F_91(x))
Eq(F_97(x), F_93(x))
Eq(F_98(x), F_12(x)*F_86(x))
Eq(F_99(x), F_100(x) + F_102(x))
Eq(F_100(x), F_101(x) + F_28(x) + F_44(x))
Eq(F_101(x), F_12(x)*F_58(x))
Eq(F_102(x), F_103(x) + 2*F_28(x) + F_79(x))
Eq(F_103(x), F_12(x)*F_99(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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 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, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": 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0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 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": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 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": 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