0231_1203_1230_3012
Counting sequence:
1, 1, 2, 6, 20, 65, 203, 624, 1933, 6119, 19893, 66379, 226618, 788544, 2786577, 9970685, 36036808, 131317866, 481761863, 1777426543, 6589175459, 24528037556, 91634857626, 343435098195, 1290829922379, 4864228954964, 18372980857291, 69547426605358, 263782163232041, 1002326567474141, 3815194475028157, 14545148811284005, 55535329153045219, 212339247574729582, 812951727735835492, 3116304444267247476, 11959845106857138230, 45950919518567023578, 176734146805884194902, 680426071998749370254, 2622128768839034705577, 10113922848600833086265, 39044440407749791420290, 150853505083339694451775, 583300183397676131712517, 2257118011392230156078217, 8740329099404467556483304, 33868774713515351453805050, 131327900600055059163647050, 509552250993152272459513421, 1978261672089845636517081691, 7684785705855037725836308032, 29869167032907691801312368906, 116157871670620145900885902005, 451959718557651152814904222384, 1759414617914826235763508051573, 6852456931064927684748293499672, 26700952864714124873286504022262, 104088460308697147067983360284334, 405944995175840155584973098473275, 1583850964715116325838790041063896, 6182127958878249462926956743807389, 24139737743769010169273864787406861, 94295850560555532949441682213579050, 368479169880214136844541828265960551, 1440418573161761962557776768840404045, 5632681584587045182391918168274270931, 22033725022022428216620726447431405065, 86218923999122793383300184308862280644, 337485502510616649761125106256105738286, 1321422108421270161281521231668734782983, 5175569924648541274534893478839333852040, 20276890389715405292047940373642327903056, 79463489365092184654478975593114190566262, 311496878311139828390372394189463189857825, 1221395654430468823061108268302916805365127, 4790408930363525840433408094103707644184665, 18793142726810431757228219398460106719423558, 73745243611533807575929517542478223450800792, 289450081175268225796472083841078066027650545, 1136359577947344473265239574169979865240558973, 4462290049988340703435444994172939006608185754, 17526585015616826690982486532191078782253981849, 68854441132780317632017237699932247836590874064, 270557451039395421106839086968846270935129226075, 1063353702922274583233919262478695542750478426371, 4180080073556526576939630684509186074046776928547, 16435314834665431339699061234978938299246189742046, 64633260585762925570674276114624654260187927714511, 254224158304000824138789218490690113344034019923182, 1000134600800354850015743917064191521872511515187510, 3935312233584004853289586266200141226919319316622544, 15487357822491889821028041738022807211817289489405060, 60960876535340416771961793210206495197986875443990804, 239993345518077007685029319350072163482768484733834740, 944973797977428214056263037537170519152505729616596484, 3721443204405954400859429184963323685506219736284302779, 14657929356129575474729167213761972574752895221347622719, 57743358069601357875170036359788923224142752426162067072, 227508830794229349891074112497900653528720203571637175617, 896519947090131497252413547825532315700061322223443423159
Generating function in Maple syntax:
1/2*(-3*(x^3-5/3*x^2+4/3*x-1/3)*(-1+x)^5*(1-4*x)^(1/2)-4*x^9+9*x^8-28*x^7+67*x^6-107*x^5+112*x^4-78*x^3+35*x^2-9*x+1)/x/(3*x^3-5*x^2+4*x-1)/(-1+x)^5
Generating function in latex syntax:
\frac{-3 \left(x^{3}-\frac{5}{3} x^{2}+\frac{4}{3} x -\frac{1}{3}\right) \left(-1+x \right)^{5} \sqrt{1-4 x}-4 x^{9}+9 x^{8}-28 x^{7}+67 x^{6}-107 x^{5}+112 x^{4}-78 x^{3}+35 x^{2}-9 x +1}{2 x \left(3 x^{3}-5 x^{2}+4 x -1\right) \left(-1+x \right)^{5}}
Generating function in sympy syntax:
(-2*x**9 + 9*x**8/2 - 14*x**7 + 67*x**6/2 - 107*x**5/2 + 56*x**4 - 39*x**3 + 35*x**2/2 - 9*x/2 + sqrt(1 - 4*x)*(x - 1)**5*(-3*x**3 + 5*x**2 - 4*x + 1)/2 + 1/2)/(x*(x - 1)**5*(3*x**3 - 5*x**2 + 4*x - 1))
Implicit equation for the generating function in Maple syntax:
x*(3*x^3-5*x^2+4*x-1)^2*(-1+x)^10*F(x)^2+(4*x^9-9*x^8+28*x^7-67*x^6+107*x^5-112*x^4+78*x^3-35*x^2+9*x-1)*(3*x^3-5*x^2+4*x-1)*(-1+x)^5*F(x)+4*x^17-9*x^16-46*x^15+524*x^14-2443*x^13+7279*x^12-15551*x^11+25134*x^10-31624*x^9+31434*x^8-24808*x^7+15497*x^6-7576*x^5+2837*x^4-785*x^3+151*x^2-18*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(3 x^{3}-5 x^{2}+4 x -1\right)^{2} \left(-1+x \right)^{10} F \! \left(x \right)^{2}+\left(4 x^{9}-9 x^{8}+28 x^{7}-67 x^{6}+107 x^{5}-112 x^{4}+78 x^{3}-35 x^{2}+9 x -1\right) \left(3 x^{3}-5 x^{2}+4 x -1\right) \left(-1+x \right)^{5} F \! \left(x \right)+4 x^{17}-9 x^{16}-46 x^{15}+524 x^{14}-2443 x^{13}+7279 x^{12}-15551 x^{11}+25134 x^{10}-31624 x^{9}+31434 x^{8}-24808 x^{7}+15497 x^{6}-7576 x^{5}+2837 x^{4}-785 x^{3}+151 x^{2}-18 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 65
a(6) = 203
a(7) = 624
a(8) = 1933
a(9) = 6119
a(10) = 19893
a(11) = 66379
a(12) = 226618
a(13) = 788544
a(n+7) = 18*(2*n+1)/(n+8)*a(n)-3*(43*n+66)/(n+8)*a(n+1)+2*(113*n+290)/(n+8)*a(n+2)-(233*n+840)/(n+8)*a(n+3)+2*(75*n+349)/(n+8)*a(n+4)-2*(29*n+166)/(n+8)*a(n+5)+2*(6*n+41)/(n+8)*a(n+6)-1/24*(3*n^5-34*n^4+205*n^3-902*n^2+704*n-336)/(n+8), n >= 14
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) = 20
a \! \left(5\right) = 65
a \! \left(6\right) = 203
a \! \left(7\right) = 624
a \! \left(8\right) = 1933
a \! \left(9\right) = 6119
a \! \left(10\right) = 19893
a \! \left(11\right) = 66379
a \! \left(12\right) = 226618
a \! \left(13\right) = 788544
a \! \left(n +7\right) = \frac{18 \left(2 n +1\right) a \! \left(n \right)}{n +8}-\frac{3 \left(43 n +66\right) a \! \left(n +1\right)}{n +8}+\frac{2 \left(113 n +290\right) a \! \left(n +2\right)}{n +8}-\frac{\left(233 n +840\right) a \! \left(n +3\right)}{n +8}+\frac{2 \left(75 n +349\right) a \! \left(n +4\right)}{n +8}-\frac{2 \left(29 n +166\right) a \! \left(n +5\right)}{n +8}+\frac{2 \left(6 n +41\right) a \! \left(n +6\right)}{n +8}-\frac{3 n^{5}-34 n^{4}+205 n^{3}-902 n^{2}+704 n -336}{24 \left(n +8\right)}, \quad n \geq 14
Specification 1
Strategy pack name: requirement_placements_tracked_fusion
Tree: http://permpal.com/tree/21453/
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[9,x]
F[4,x] = F[100,x]+F[5,x]
F[5,x] = F[10,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[6,x]*F[9,x]
F[9,x] = x
F[10,x] = F[11,x]+F[37,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[9,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[1,x]+F[11,x]
F[15,x] = F[16,x]+F[25,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[9,x]
F[18,x] = F[19,x]+F[6,x]
F[19,x] = F[16,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[9,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[7,x]
F[24,x] = F[20,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]*F[9,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[11,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[28,x]*F[9,x]
F[31,x] = F[25,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[9,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[29,x]
F[36,x] = F[32,x]
F[37,x] = F[38,x]+F[39,x]+F[84,x]
F[38,x] = 0
F[39,x] = F[40,x]*F[9,x]
F[40,x] = F[41,x]+F[73,x]
F[41,x] = F[42,x]+F[7,x]
F[42,x] = F[38,x]+F[43,x]+F[70,x]
F[43,x] = F[44,x]*F[9,x]
F[44,x] = F[41,x]+F[45,x]
F[45,x] = F[46,x]+F[58,x]
F[46,x] = F[47,x]
F[47,x] = F[48,x]*F[9,x]
F[48,x] = F[49,x]+F[52,x]
F[49,x] = F[50,x]+F[7,x]
F[50,x] = F[51,x]
F[51,x] = F[49,x]*F[9,x]
F[52,x] = F[46,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[55,x]*F[9,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[50,x]
F[57,x] = F[53,x]
F[58,x] = F[59,x]
F[59,x] = F[60,x]*F[9,x]
F[60,x] = F[61,x]+F[64,x]
F[61,x] = F[42,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[61,x]*F[9,x]
F[64,x] = F[58,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[67,x]*F[9,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[62,x]
F[69,x] = F[65,x]
F[70,x] = F[71,x]*F[9,x]
F[71,x] = F[7,x]+F[72,x]
F[72,x] = F[38,x]+F[51,x]+F[70,x]
F[73,x] = F[74,x]+F[89,x]
F[74,x] = F[38,x]+F[75,x]+F[84,x]
F[75,x] = F[76,x]*F[9,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[7,x]+F[72,x]
F[78,x] = F[74,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[81,x]*F[9,x]
F[81,x] = F[82,x]+F[83,x]
F[82,x] = F[72,x]
F[83,x] = F[79,x]
F[84,x] = F[85,x]*F[9,x]
F[85,x] = F[7,x]+F[86,x]
F[86,x] = F[38,x]+F[84,x]+F[87,x]
F[87,x] = F[88,x]*F[9,x]
F[88,x] = F[7,x]+F[86,x]
F[89,x] = F[90,x]
F[90,x] = F[9,x]*F[91,x]
F[91,x] = F[92,x]+F[94,x]
F[92,x] = F[42,x]+F[93,x]
F[93,x] = F[63,x]
F[94,x] = F[89,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[9,x]*F[97,x]
F[97,x] = F[98,x]+F[99,x]
F[98,x] = F[93,x]
F[99,x] = F[95,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x,1]
F[102,x,k[0]] = F[103,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]*F[114,x,k[0]]*F[9,x]
F[105,x,k[0]] = F[106,x,k[0]]+F[124,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]+F[85,x]
F[107,x,k[0]] = F[108,x,k[0]]+F[115,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]*F[9,x]
F[110,x,k[0]] = F[108,x,k[0]]+F[111,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]*F[114,x,k[0]]
F[113,x,k[0]] = k[0]*x
F[114,x,k[0]] = F[1,x]+F[111,x,k[0]]
F[115,x,k[0]] = 2*F[38,x]+F[116,x,k[0]]+F[123,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]*F[9,x]
F[117,x,k[0]] = F[115,x,k[0]]+F[118,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]+F[121,x,k[0]]+F[38,x]
F[119,x,k[0]] = F[113,x,k[0]]*F[120,x,k[0]]
F[120,x,k[0]] = F[118,x,k[0]]+F[7,x]
F[121,x,k[0]] = F[122,x,k[0]]*F[9,x]
F[122,x,k[0]] = F[111,x,k[0]]+F[118,x,k[0]]
F[123,x,k[0]] = F[107,x,k[0]]*F[9,x]
F[124,x,k[0]] = (F[103,x,k[0]]*k[0]-F[103,x,1])/(-1+k[0])
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_{9}\! \left(x \right)
F_{4}\! \left(x \right) = F_{100}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{10}\! \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_{6}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = x
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{37}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{9}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{25}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{9}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{6}\! \left(x \right)
F_{19}\! \left(x \right) = F_{16}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{9}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{7}\! \left(x \right)
F_{24}\! \left(x \right) = F_{20}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{9}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{11}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{28}\! \left(x \right) F_{9}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{9}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right)
F_{36}\! \left(x \right) = F_{32}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)+F_{84}\! \left(x \right)
F_{38}\! \left(x \right) = 0
F_{39}\! \left(x \right) = F_{40}\! \left(x \right) F_{9}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{73}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{7}\! \left(x \right)
F_{42}\! \left(x \right) = F_{38}\! \left(x \right)+F_{43}\! \left(x \right)+F_{70}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right) F_{9}\! \left(x \right)
F_{44}\! \left(x \right) = F_{41}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{58}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right) F_{9}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{52}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{7}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{49}\! \left(x \right) F_{9}\! \left(x \right)
F_{52}\! \left(x \right) = F_{46}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right) F_{9}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{50}\! \left(x \right)
F_{57}\! \left(x \right) = F_{53}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right) F_{9}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{64}\! \left(x \right)
F_{61}\! \left(x \right) = F_{42}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{61}\! \left(x \right) F_{9}\! \left(x \right)
F_{64}\! \left(x \right) = F_{58}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right) F_{9}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{62}\! \left(x \right)
F_{69}\! \left(x \right) = F_{65}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right) F_{9}\! \left(x \right)
F_{71}\! \left(x \right) = F_{7}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{38}\! \left(x \right)+F_{51}\! \left(x \right)+F_{70}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{89}\! \left(x \right)
F_{74}\! \left(x \right) = F_{38}\! \left(x \right)+F_{75}\! \left(x \right)+F_{84}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right) F_{9}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{7}\! \left(x \right)+F_{72}\! \left(x \right)
F_{78}\! \left(x \right) = F_{74}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right) F_{9}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{83}\! \left(x \right)
F_{82}\! \left(x \right) = F_{72}\! \left(x \right)
F_{83}\! \left(x \right) = F_{79}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right) F_{9}\! \left(x \right)
F_{85}\! \left(x \right) = F_{7}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{38}\! \left(x \right)+F_{84}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right) F_{9}\! \left(x \right)
F_{88}\! \left(x \right) = F_{7}\! \left(x \right)+F_{86}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{9}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{94}\! \left(x \right)
F_{92}\! \left(x \right) = F_{42}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{63}\! \left(x \right)
F_{94}\! \left(x \right) = F_{89}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{9}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)+F_{99}\! \left(x \right)
F_{98}\! \left(x \right) = F_{93}\! \left(x \right)
F_{99}\! \left(x \right) = F_{95}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x , 1\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{114}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{124}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{85}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{111}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{114}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = y x
F_{114}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{111}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = 2 F_{38}\! \left(x \right)+F_{116}\! \left(x , y\right)+F_{123}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{118}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{121}\! \left(x , y\right)+F_{38}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{120}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{7}\! \left(x \right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{118}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{124}\! \left(x , y\right) = \frac{F_{103}\! \left(x , y\right) y -F_{103}\! \left(x , 1\right)}{-1+y}
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_9(x))
Eq(F_4(x), F_100(x) + F_5(x))
Eq(F_5(x), F_10(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_6(x)*F_9(x))
Eq(F_9(x), x)
Eq(F_10(x), F_11(x) + F_37(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_9(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_1(x) + F_11(x))
Eq(F_15(x), F_16(x) + F_25(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_9(x))
Eq(F_18(x), F_19(x) + F_6(x))
Eq(F_19(x), F_16(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_9(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_7(x))
Eq(F_24(x), F_20(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x)*F_9(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_11(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_28(x)*F_9(x))
Eq(F_31(x), F_25(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_9(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_29(x))
Eq(F_36(x), F_32(x))
Eq(F_37(x), F_38(x) + F_39(x) + F_84(x))
Eq(F_38(x), 0)
Eq(F_39(x), F_40(x)*F_9(x))
Eq(F_40(x), F_41(x) + F_73(x))
Eq(F_41(x), F_42(x) + F_7(x))
Eq(F_42(x), F_38(x) + F_43(x) + F_70(x))
Eq(F_43(x), F_44(x)*F_9(x))
Eq(F_44(x), F_41(x) + F_45(x))
Eq(F_45(x), F_46(x) + F_58(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_48(x)*F_9(x))
Eq(F_48(x), F_49(x) + F_52(x))
Eq(F_49(x), F_50(x) + F_7(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_49(x)*F_9(x))
Eq(F_52(x), F_46(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_55(x)*F_9(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_50(x))
Eq(F_57(x), F_53(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_60(x)*F_9(x))
Eq(F_60(x), F_61(x) + F_64(x))
Eq(F_61(x), F_42(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_61(x)*F_9(x))
Eq(F_64(x), F_58(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_67(x)*F_9(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_62(x))
Eq(F_69(x), F_65(x))
Eq(F_70(x), F_71(x)*F_9(x))
Eq(F_71(x), F_7(x) + F_72(x))
Eq(F_72(x), F_38(x) + F_51(x) + F_70(x))
Eq(F_73(x), F_74(x) + F_89(x))
Eq(F_74(x), F_38(x) + F_75(x) + F_84(x))
Eq(F_75(x), F_76(x)*F_9(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_7(x) + F_72(x))
Eq(F_78(x), F_74(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_81(x)*F_9(x))
Eq(F_81(x), F_82(x) + F_83(x))
Eq(F_82(x), F_72(x))
Eq(F_83(x), F_79(x))
Eq(F_84(x), F_85(x)*F_9(x))
Eq(F_85(x), F_7(x) + F_86(x))
Eq(F_86(x), F_38(x) + F_84(x) + F_87(x))
Eq(F_87(x), F_88(x)*F_9(x))
Eq(F_88(x), F_7(x) + F_86(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_9(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_94(x))
Eq(F_92(x), F_42(x) + F_93(x))
Eq(F_93(x), F_63(x))
Eq(F_94(x), F_89(x) + F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_9(x)*F_97(x))
Eq(F_97(x), F_98(x) + F_99(x))
Eq(F_98(x), F_93(x))
Eq(F_99(x), F_95(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x, 1))
Eq(F_102(x, k_0), F_103(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0)*F_114(x, k_0)*F_9(x))
Eq(F_105(x, k_0), F_106(x, k_0) + F_124(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0) + F_85(x))
Eq(F_107(x, k_0), F_108(x, k_0) + F_115(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0)*F_9(x))
Eq(F_110(x, k_0), F_108(x, k_0) + F_111(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0)*F_114(x, k_0))
Eq(F_113(x, k_0), k_0*x)
Eq(F_114(x, k_0), F_1(x) + F_111(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0) + F_123(x, k_0) + 2*F_38(x))
Eq(F_116(x, k_0), F_117(x, k_0)*F_9(x))
Eq(F_117(x, k_0), F_115(x, k_0) + F_118(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0) + F_121(x, k_0) + F_38(x))
Eq(F_119(x, k_0), F_113(x, k_0)*F_120(x, k_0))
Eq(F_120(x, k_0), F_118(x, k_0) + F_7(x))
Eq(F_121(x, k_0), F_122(x, k_0)*F_9(x))
Eq(F_122(x, k_0), F_111(x, k_0) + F_118(x, k_0))
Eq(F_123(x, k_0), F_107(x, k_0)*F_9(x))
Eq(F_124(x, k_0), (-k_0*F_103(x, k_0) + F_103(x, 1))/(1 - k_0))
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, 2, 3, 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]]}, {"patt": [3, 0, 1, 2], "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, 2, 3, 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]]}, {"patt": [3, 0, 1, 2], "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, 3, 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]]}, {"patt": [3, 0, 1, 2], "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": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [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": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "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, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": 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