0123_0132_0231_1023_1230_2013

Counting sequence:
1, 1, 2, 6, 18, 54, 166, 527, 1724, 5781, 19770, 68677, 241616, 859003, 3081054, 11134870, 40505546, 148195362, 544949638, 2012979284, 7465880370, 27791334016, 103795058102, 388825802598, 1460606594398, 5500644720302, 20763951410102, 78549995674506, 297751596001566, 1130766611311282, 4301779598911286, 16391940054856327, 62556866313580356, 239079065308904917, 914941175383570418, 3505872956890561873, 13449920218742865824, 51657746023310607679, 198617422737362473190, 764436354256620221019, 2944999310166431879688, 11356077516621109055517, 43828002536257418140186, 169292384120445987235115, 654438786711269434015164, 2531809762603518271194253, 9801873981060437738088302, 37974290241796553457826641, 147217714653386287662790540, 571095135274636522739238191, 2216785519777151866286226954, 8609842749640896563925700105, 33459018899760955748493507368, 130097303955146830053791957799, 506117898018466559205877060918, 1969949415546263084956330712921, 7671328063757202309166702096140, 29887574946270884184507937215343, 116495290260046913279956366249922, 454272985836705023847542042852781, 1772188576332573813707610249384472, 6916420186476212140142500631788931, 27003835551688006076688233424111822, 105471881906750237450720595764700886, 412106872506176422379314148018623274, 1610793797622432916798250278982077362, 6298283500748796127424140412734039750, 24634972203012890669165731537332392588, 96388498029444861480363689509216244226, 377257128412085271322691264836870403464, 1477014710192496571993764711772039074902, 5784469004798880842217461585231931622890, 22660518056663018397512160993336792853078, 88797415543477945186994981285271772349066, 348057993390660237157455614967826630154694, 1364647447776169454364020862885423888465862, 5351848280286431601516523458219579614273990, 20994165287740728124881136359867475872865158, 82376258313834321780169950974777339906340886, 323304230745747667120785030468058403112037724, 1269182105997532402403845598616320046935235242, 4983531037693494875195449402320361495451644080, 19572604040924265761658976882937127126700205598, 76887528245678318651466757957403494995140814136, 302104191255500653823611179287532446271074759474, 1187268537374366978327283436152138017714739960652, 4666920453284000601456863131679035262982292227990, 18348434462590559224572269447713956652206139070668, 72152739535442228093075414984711102134233843013106, 283785311410099718338677016249783304064181029250024, 1116370688648636226206764261466006439108857631906542, 4392447414478469448681813459930178649375738478738460, 17285526697232892271308280977719078800833409273259978, 68035391337511961401976365294307640399781010079595896, 267831564070170983012891753000270313685097842814956614, 1054536596814785033641506585075878435579023236623638182, 4152723929046651064466611770867807469520555466317665150, 16355901804551040176886065461468155139430490768623866718, 64429465446209544968587205149555786939354261188644557686, 253841002455153834731766239710560625550704160862492584194, 1000241541104973637422851664770374101338849680121517647342

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

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

Generating function in sympy syntax:
(-x**3 + x**2 - x + sqrt(1 - 4*x)*(-2*x**2 + 2*x - 1)/2 + 1/2)/(x*(x - 1)**2)

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

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

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 18
a(5) = 54
a(n+4) = -4*(2*n+1)/(n+5)*a(n)+2*(9*n+10)/(n+5)*a(1+n)-8*(2*n+5)/(n+5)*a(n+2)+(26+7*n)/(n+5)*a(n+3)+2/(n+5), n >= 6

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) = 18
a \! \left(5\right) = 54
a \! \left(n +4\right) = -\frac{4 \left(2 n +1\right) a \! \left(n \right)}{n +5}+\frac{2 \left(9 n +10\right) a \! \left(1+n \right)}{n +5}-\frac{8 \left(2 n +5\right) a \! \left(n +2\right)}{n +5}+\frac{\left(26+7 n \right) a \! \left(n +3\right)}{n +5}+\frac{2}{n +5}, \quad n \geq 6

Specification 1
Strategy pack name: requirement_placements_tracked_fusion
Tree: http://www.permpal.com/tree/22079/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[6,x]
F[1,x] = F[2,x]+F[3,x]
F[2,x] = 1
F[3,x] = F[4,x]
F[4,x] = F[1,x]*F[5,x]
F[5,x] = x
F[6,x] = F[7,x]
F[7,x] = F[5,x]*F[8,x]
F[8,x] = F[39,x]+F[9,x]
F[9,x] = F[10,x]+F[20,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[5,x]
F[12,x] = F[13,x]+F[14,x]
F[13,x] = F[2,x]+F[5,x]
F[14,x] = F[10,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[5,x]
F[17,x] = F[18,x]+F[19,x]
F[18,x] = F[5,x]
F[19,x] = F[15,x]
F[20,x] = F[21,x]+F[22,x]+F[27,x]
F[21,x] = 0
F[22,x] = F[23,x]*F[5,x]
F[23,x] = F[24,x]+F[3,x]
F[24,x] = F[21,x]+F[22,x]+F[25,x]
F[25,x] = F[26,x]*F[5,x]
F[26,x] = F[24,x]+F[3,x]
F[27,x] = F[28,x]*F[5,x]
F[28,x] = F[29,x]+F[33,x]
F[29,x] = F[3,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[5,x]
F[32,x] = F[30,x]+F[5,x]
F[33,x] = F[20,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[5,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[30,x]
F[38,x] = F[34,x]
F[39,x] = F[40,x]
F[40,x] = F[41,x]*F[5,x]
F[41,x] = F[42,x]+F[79,x]
F[42,x] = F[43,x]+F[59,x]
F[43,x] = F[44,x]+F[50,x]
F[44,x] = F[45,x]
F[45,x] = F[46,x]*F[5,x]
F[46,x] = F[1,x]+F[47,x]
F[47,x] = F[3,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[47,x]*F[5,x]
F[50,x] = F[21,x]+F[51,x]+F[58,x]
F[51,x] = F[5,x]*F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = F[3,x]+F[48,x]
F[54,x] = F[24,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[5,x]*F[57,x]
F[57,x] = F[48,x]+F[55,x]
F[58,x] = F[43,x]*F[5,x]
F[59,x] = F[50,x]+F[60,x]
F[60,x] = F[21,x]+F[61,x]+F[76,x]+F[78,x]
F[61,x] = F[5,x]*F[62,x]
F[62,x] = F[63,x]+F[67,x]
F[63,x] = F[48,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[5,x]*F[66,x]
F[66,x] = F[48,x]+F[64,x]
F[67,x] = F[68,x]+F[73,x]
F[68,x] = 2*F[21,x]+F[69,x]+F[71,x]
F[69,x] = F[5,x]*F[70,x]
F[70,x] = F[48,x]+F[68,x]
F[71,x] = F[5,x]*F[72,x]
F[72,x] = F[24,x]+F[68,x]
F[73,x] = F[74,x]
F[74,x] = F[5,x]*F[75,x]
F[75,x] = F[55,x]+F[73,x]
F[76,x] = F[5,x]*F[77,x]
F[77,x] = F[50,x]+F[60,x]
F[78,x] = F[5,x]*F[59,x]
F[79,x] = F[80,x]
F[80,x] = F[81,x,1]
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[5,x]*F[84,x,k[0]]
F[84,x,k[0]] = F[134,x,k[0]]+F[85,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]*F[90,x,k[0]]
F[86,x,k[0]] = F[2,x]+F[87,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[86,x,k[0]]*F[89,x,k[0]]
F[89,x,k[0]] = k[0]*x
F[90,x,k[0]] = F[100,x,k[0]]+F[91,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]+F[95,x,k[0]]
F[92,x,k[0]] = F[3,x]+F[93,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]
F[94,x,k[0]] = F[89,x,k[0]]*F[92,x,k[0]]
F[95,x,k[0]] = F[24,x]+F[96,x,k[0]]
F[96,x,k[0]] = 2*F[21,x]+F[97,x,k[0]]+F[99,x,k[0]]
F[97,x,k[0]] = F[5,x]*F[98,x,k[0]]
F[98,x,k[0]] = F[93,x,k[0]]+F[96,x,k[0]]
F[99,x,k[0]] = F[89,x,k[0]]*F[95,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]+F[114,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]+F[50,x]
F[102,x,k[0]] = 2*F[21,x]+F[103,x,k[0]]+F[113,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]*F[5,x]
F[104,x,k[0]] = F[105,x,k[0]]+F[109,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]+F[93,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]*F[89,x,k[0]]
F[108,x,k[0]] = F[106,x,k[0]]+F[48,x]
F[109,x,k[0]] = F[110,x,k[0]]+F[96,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]*F[89,x,k[0]]
F[112,x,k[0]] = F[110,x,k[0]]+F[55,x]
F[113,x,k[0]] = F[101,x,k[0]]*F[89,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]+F[60,x]
F[115,x,k[0]] = 2*F[21,x]+F[116,x,k[0]]+F[131,x,k[0]]+F[133,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]*F[5,x]
F[117,x,k[0]] = F[118,x,k[0]]+F[122,x,k[0]]
F[118,x,k[0]] = F[106,x,k[0]]+F[119,x,k[0]]
F[119,x,k[0]] = F[120,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]*F[89,x,k[0]]
F[121,x,k[0]] = F[119,x,k[0]]+F[64,x]
F[122,x,k[0]] = F[123,x,k[0]]+F[128,x,k[0]]
F[123,x,k[0]] = 3*F[21,x]+F[124,x,k[0]]+F[126,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]*F[5,x]
F[125,x,k[0]] = F[106,x,k[0]]+F[123,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]*F[89,x,k[0]]
F[127,x,k[0]] = F[123,x,k[0]]+F[68,x]
F[128,x,k[0]] = F[129,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]*F[89,x,k[0]]
F[130,x,k[0]] = F[128,x,k[0]]+F[73,x]
F[131,x,k[0]] = F[132,x,k[0]]*F[5,x]
F[132,x,k[0]] = F[102,x,k[0]]+F[115,x,k[0]]
F[133,x,k[0]] = F[114,x,k[0]]*F[89,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]*F[86,x,k[0]]
F[135,x,k[0]] = 1/(-1+k[0])*(F[82,x,k[0]]*k[0]-F[82,x,1])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{1}\! \left(x \right) = F_{2}\! \left(x \right)+F_{3}\! \left(x \right)
F_{2}\! \left(x \right) = 1
F_{3}\! \left(x \right) = F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = x
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{39}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{20}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{5}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{14}\! \left(x \right)
F_{13}\! \left(x \right) = F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{14}\! \left(x \right) = F_{10}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{5}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{5}\! \left(x \right)
F_{19}\! \left(x \right) = F_{15}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)+F_{27}\! \left(x \right)
F_{21}\! \left(x \right) = 0
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{5}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{3}\! \left(x \right)
F_{24}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{5}\! \left(x \right)
F_{26}\! \left(x \right) = F_{24}\! \left(x \right)+F_{3}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{5}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{33}\! \left(x \right)
F_{29}\! \left(x \right) = F_{3}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{5}\! \left(x \right)
F_{32}\! \left(x \right) = F_{30}\! \left(x \right)+F_{5}\! \left(x \right)
F_{33}\! \left(x \right) = F_{20}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{5}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{30}\! \left(x \right)
F_{38}\! \left(x \right) = F_{34}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right) F_{5}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{79}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{59}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{50}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right) F_{5}\! \left(x \right)
F_{46}\! \left(x \right) = F_{1}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{3}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{47}\! \left(x \right) F_{5}\! \left(x \right)
F_{50}\! \left(x \right) = F_{21}\! \left(x \right)+F_{51}\! \left(x \right)+F_{58}\! \left(x \right)
F_{51}\! \left(x \right) = F_{5}\! \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_{3}\! \left(x \right)+F_{48}\! \left(x \right)
F_{54}\! \left(x \right) = F_{24}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{5}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{48}\! \left(x \right)+F_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{43}\! \left(x \right) F_{5}\! \left(x \right)
F_{59}\! \left(x \right) = F_{50}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{21}\! \left(x \right)+F_{61}\! \left(x \right)+F_{76}\! \left(x \right)+F_{78}\! \left(x \right)
F_{61}\! \left(x \right) = F_{5}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{67}\! \left(x \right)
F_{63}\! \left(x \right) = F_{48}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{5}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{48}\! \left(x \right)+F_{64}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{73}\! \left(x \right)
F_{68}\! \left(x \right) = 2 F_{21}\! \left(x \right)+F_{69}\! \left(x \right)+F_{71}\! \left(x \right)
F_{69}\! \left(x \right) = F_{5}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{48}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{5}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{24}\! \left(x \right)+F_{68}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{5}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{55}\! \left(x \right)+F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{5}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{50}\! \left(x \right)+F_{60}\! \left(x \right)
F_{78}\! \left(x \right) = F_{5}\! \left(x \right) F_{59}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x , 1\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right) F_{90}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{86}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = y x
F_{90}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{3}\! \left(x \right)+F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{89}\! \left(x , y\right) F_{92}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = 2 F_{21}\! \left(x \right)+F_{97}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{93}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{89}\! \left(x , y\right) F_{95}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{114}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{50}\! \left(x \right)
F_{102}\! \left(x , y\right) = 2 F_{21}\! \left(x \right)+F_{103}\! \left(x , y\right)+F_{113}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{109}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{48}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{55}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{60}\! \left(x \right)
F_{115}\! \left(x , y\right) = 2 F_{21}\! \left(x \right)+F_{116}\! \left(x , y\right)+F_{131}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{122}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{119}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{64}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{128}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = 3 F_{21}\! \left(x \right)+F_{124}\! \left(x , y\right)+F_{126}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{125}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{123}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{68}\! \left(x \right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{73}\! \left(x \right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{132}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right) F_{86}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = -\frac{-y F_{82}\! \left(x , y\right)+F_{82}\! \left(x , 1\right)}{-1+y}
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_6(x))
Eq(F_1(x), F_2(x) + F_3(x))
Eq(F_2(x), 1)
Eq(F_3(x), F_4(x))
Eq(F_4(x), F_1(x)*F_5(x))
Eq(F_5(x), x)
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_5(x)*F_8(x))
Eq(F_8(x), F_39(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_20(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_5(x))
Eq(F_12(x), F_13(x) + F_14(x))
Eq(F_13(x), F_2(x) + F_5(x))
Eq(F_14(x), F_10(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_5(x))
Eq(F_17(x), F_18(x) + F_19(x))
Eq(F_18(x), F_5(x))
Eq(F_19(x), F_15(x))
Eq(F_20(x), F_21(x) + F_22(x) + F_27(x))
Eq(F_21(x), 0)
Eq(F_22(x), F_23(x)*F_5(x))
Eq(F_23(x), F_24(x) + F_3(x))
Eq(F_24(x), F_21(x) + F_22(x) + F_25(x))
Eq(F_25(x), F_26(x)*F_5(x))
Eq(F_26(x), F_24(x) + F_3(x))
Eq(F_27(x), F_28(x)*F_5(x))
Eq(F_28(x), F_29(x) + F_33(x))
Eq(F_29(x), F_3(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_5(x))
Eq(F_32(x), F_30(x) + F_5(x))
Eq(F_33(x), F_20(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_5(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_30(x))
Eq(F_38(x), F_34(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_41(x)*F_5(x))
Eq(F_41(x), F_42(x) + F_79(x))
Eq(F_42(x), F_43(x) + F_59(x))
Eq(F_43(x), F_44(x) + F_50(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_46(x)*F_5(x))
Eq(F_46(x), F_1(x) + F_47(x))
Eq(F_47(x), F_3(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_47(x)*F_5(x))
Eq(F_50(x), F_21(x) + F_51(x) + F_58(x))
Eq(F_51(x), F_5(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), F_3(x) + F_48(x))
Eq(F_54(x), F_24(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_5(x)*F_57(x))
Eq(F_57(x), F_48(x) + F_55(x))
Eq(F_58(x), F_43(x)*F_5(x))
Eq(F_59(x), F_50(x) + F_60(x))
Eq(F_60(x), F_21(x) + F_61(x) + F_76(x) + F_78(x))
Eq(F_61(x), F_5(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_67(x))
Eq(F_63(x), F_48(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_5(x)*F_66(x))
Eq(F_66(x), F_48(x) + F_64(x))
Eq(F_67(x), F_68(x) + F_73(x))
Eq(F_68(x), 2*F_21(x) + F_69(x) + F_71(x))
Eq(F_69(x), F_5(x)*F_70(x))
Eq(F_70(x), F_48(x) + F_68(x))
Eq(F_71(x), F_5(x)*F_72(x))
Eq(F_72(x), F_24(x) + F_68(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_5(x)*F_75(x))
Eq(F_75(x), F_55(x) + F_73(x))
Eq(F_76(x), F_5(x)*F_77(x))
Eq(F_77(x), F_50(x) + F_60(x))
Eq(F_78(x), F_5(x)*F_59(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_81(x, 1))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_5(x)*F_84(x, k_0))
Eq(F_84(x, k_0), F_134(x, k_0) + F_85(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0)*F_90(x, k_0))
Eq(F_86(x, k_0), F_2(x) + F_87(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_86(x, k_0)*F_89(x, k_0))
Eq(F_89(x, k_0), k_0*x)
Eq(F_90(x, k_0), F_100(x, k_0) + F_91(x, k_0))
Eq(F_91(x, k_0), F_92(x, k_0) + F_95(x, k_0))
Eq(F_92(x, k_0), F_3(x) + F_93(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_94(x, k_0), F_89(x, k_0)*F_92(x, k_0))
Eq(F_95(x, k_0), F_24(x) + F_96(x, k_0))
Eq(F_96(x, k_0), 2*F_21(x) + F_97(x, k_0) + F_99(x, k_0))
Eq(F_97(x, k_0), F_5(x)*F_98(x, k_0))
Eq(F_98(x, k_0), F_93(x, k_0) + F_96(x, k_0))
Eq(F_99(x, k_0), F_89(x, k_0)*F_95(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_114(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0) + F_50(x))
Eq(F_102(x, k_0), F_103(x, k_0) + F_113(x, k_0) + 2*F_21(x))
Eq(F_103(x, k_0), F_104(x, k_0)*F_5(x))
Eq(F_104(x, k_0), F_105(x, k_0) + F_109(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0) + F_93(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0)*F_89(x, k_0))
Eq(F_108(x, k_0), F_106(x, k_0) + F_48(x))
Eq(F_109(x, k_0), F_110(x, k_0) + F_96(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0)*F_89(x, k_0))
Eq(F_112(x, k_0), F_110(x, k_0) + F_55(x))
Eq(F_113(x, k_0), F_101(x, k_0)*F_89(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0) + F_60(x))
Eq(F_115(x, k_0), F_116(x, k_0) + F_131(x, k_0) + F_133(x, k_0) + 2*F_21(x))
Eq(F_116(x, k_0), F_117(x, k_0)*F_5(x))
Eq(F_117(x, k_0), F_118(x, k_0) + F_122(x, k_0))
Eq(F_118(x, k_0), F_106(x, k_0) + F_119(x, k_0))
Eq(F_119(x, k_0), F_120(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0)*F_89(x, k_0))
Eq(F_121(x, k_0), F_119(x, k_0) + F_64(x))
Eq(F_122(x, k_0), F_123(x, k_0) + F_128(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0) + F_126(x, k_0) + 3*F_21(x))
Eq(F_124(x, k_0), F_125(x, k_0)*F_5(x))
Eq(F_125(x, k_0), F_106(x, k_0) + F_123(x, k_0))
Eq(F_126(x, k_0), F_127(x, k_0)*F_89(x, k_0))
Eq(F_127(x, k_0), F_123(x, k_0) + F_68(x))
Eq(F_128(x, k_0), F_129(x, k_0))
Eq(F_129(x, k_0), F_130(x, k_0)*F_89(x, k_0))
Eq(F_130(x, k_0), F_128(x, k_0) + F_73(x))
Eq(F_131(x, k_0), F_132(x, k_0)*F_5(x))
Eq(F_132(x, k_0), F_102(x, k_0) + F_115(x, k_0))
Eq(F_133(x, k_0), F_114(x, k_0)*F_89(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0)*F_86(x, k_0))
Eq(F_135(x, k_0), (k_0*F_82(x, k_0) - F_82(x, 1))/(k_0 - 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "limited_insertion": true, "maxreqlen": 2, "strategy_class": "RequirementInsertionFactory"}, {"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.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "requirement_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "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, 1, 3, 2], "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, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": 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