0213_0231_1230_3012
Counting sequence:
1, 1, 2, 6, 20, 64, 195, 585, 1783, 5617, 18356, 61945, 214340, 755512, 2699533, 9744771, 35457081, 129842927, 478033970, 1768052319, 6565696758, 24469417150, 91488860595, 343072203346, 1289929321425, 4861996743099, 18367453747420, 69533752256815, 263748354420308, 1002243021977368, 3814988112727889, 14544639260478823, 55534071319529581, 212336143297179867, 812944067919574302, 3116285546446953963, 11959798488939719658, 45950804530780230106, 176733863199323626415, 680425372554609593514, 2622127043925759631133, 10113918594936433107055, 39044429918501513825400, 150853479218279491304091, 583300119619384972276136, 2257117854130024631520692, 8740328711638726506459693, 33868773757402153119123456, 131327898242591577943233943, 509552245180461562984932717, 1978261657757849503484247766, 7684785670517694084951571725, 29869166945779381349583720450, 116157871455795945049436225282, 451959718027980493045374022307, 1759414616608872914188008635148, 6852456927844981583940715694133, 26700952856775068077027335060511, 104088460289122736379062546771340, 405944995127577850421771898923131, 1583850964596121772069029689760884, 6182127958584859109251594668241176, 24139737743045633743240486187873177, 94295850558771993622993440229097711, 368479169875816687149125153278465941, 1440418573150919724212722115373151347, 5632681584560312845674380148107127478, 22033725021956517684719481498572285571, 86218923998960286168907498432731109138, 337485502510215976442227508993117911890, 1321422108420282272260829608266347359335, 5175569924646105562960715056147300538474, 20276890389709399870012548292559109812693, 79463489365077377855375337080958205549047, 311496878311103321165870490416027006392368, 1221395654430378811885429119802397874500371, 4790408930363303911441723003983735947362896, 18793142726809884575438034870265288164784492, 73745243611532458460143499037002815181197605, 289450081175264899455190540394201739146842044, 1136359577947336271933446265734089400431169303, 4462290049988320482466868074964977071025348285, 17526585015616776834742394072833343411446128350, 68854441132780194707902559144504022693083422381, 270557451039395118028671477508839317520866059226, 1063353702922273835973094686482817960923491223242, 4180080073556524734514811885049590462829525124603, 16435314834665426797069377074520252152169136096716, 64633260585762914370497101713660913480284624650733, 254224158304000796523954369233871111121753548693735, 1000134600800354781929401107446600792432873441070660, 3935312233584004685417857286583467365914856379943379, 15487357822491889407128334391418578944295580525245148, 60960876535340415751462578436110120316533027699714192, 239993345518077005168915806334037665855407425070121873, 944973797977428207852605929876061482535483953395907276, 3721443204405954385563870660221490431106013087697794131, 14657929356129575437016878084341520304505967731534918657, 57743358069601357782187701083411831419606757186023768250, 227508830794229349661819541346426804127213733724072053849, 896519947090131496687170071975576532763181623783804471758
Generating function in Maple syntax:
1/2*(-2*(x-1/2)*(-1+x)^5*(1-4*x)^(1/2)-2*x^7+2*x^6-13*x^5+27*x^4-30*x^3+20*x^2-7*x+1)/x/(2*x-1)/(-1+x)^5
Generating function in latex syntax:
\frac{-2 \left(x -\frac{1}{2}\right) \left(-1+x \right)^{5} \sqrt{1-4 x}-2 x^{7}+2 x^{6}-13 x^{5}+27 x^{4}-30 x^{3}+20 x^{2}-7 x +1}{2 x \left(2 x -1\right) \left(-1+x \right)^{5}}
Generating function in sympy syntax:
(-x**7 + x**6 - 13*x**5/2 + 27*x**4/2 - 15*x**3 + 10*x**2 - 7*x/2 + sqrt(1 - 4*x)*(1 - 2*x)*(x - 1)**5/2 + 1/2)/(x*(x - 1)**5*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*(-1+x)^10*F(x)^2+(2*x-1)*(2*x^7-2*x^6+13*x^5-27*x^4+30*x^3-20*x^2+7*x-1)*(-1+x)^5*F(x)+x^13+2*x^12-31*x^11+192*x^10-626*x^9+1307*x^8-1905*x^7+2007*x^6-1545*x^5+862*x^4-339*x^3+89*x^2-14*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} \left(-1+x \right)^{10} F \! \left(x \right)^{2}+\left(2 x -1\right) \left(2 x^{7}-2 x^{6}+13 x^{5}-27 x^{4}+30 x^{3}-20 x^{2}+7 x -1\right) \left(-1+x \right)^{5} F \! \left(x \right)+x^{13}+2 x^{12}-31 x^{11}+192 x^{10}-626 x^{9}+1307 x^{8}-1905 x^{7}+2007 x^{6}-1545 x^{5}+862 x^{4}-339 x^{3}+89 x^{2}-14 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 64
a(6) = 195
a(7) = 585
a(8) = 1783
a(9) = 5617
a(n+3) = 8*(2*n+1)/(n+4)*a(n)-4*(5*n+8)/(n+4)*a(n+1)+2*(4*n+11)/(n+4)*a(n+2)-1/24*n*(n-1)*(n-6)*(3*n^2-43*n+2)/(n+4), n >= 10
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) = 64
a \! \left(6\right) = 195
a \! \left(7\right) = 585
a \! \left(8\right) = 1783
a \! \left(9\right) = 5617
a \! \left(n +3\right) = \frac{8 \left(2 n +1\right) a \! \left(n \right)}{n +4}-\frac{4 \left(5 n +8\right) a \! \left(n +1\right)}{n +4}+\frac{2 \left(4 n +11\right) a \! \left(n +2\right)}{n +4}-\frac{n \left(n -1\right) \left(n -6\right) \left(3 n^{2}-43 n +2\right)}{24 \left(n +4\right)}, \quad n \geq 10
Specification 1
Strategy pack name: requirement_placements_tracked_fusion
Tree: http://permpal.com/tree/21337/
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[126,x]+F[9,x]
F[9,x] = F[10,x]+F[52,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[5,x]
F[12,x] = F[13,x]+F[16,x]
F[13,x] = F[14,x]+F[2,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[5,x]
F[16,x] = F[17,x]+F[29,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[5,x]
F[19,x] = F[20,x]+F[21,x]
F[20,x] = F[2,x]+F[5,x]
F[21,x] = F[17,x]+F[22,x]
F[22,x] = F[23,x]+F[24,x]+F[28,x]
F[23,x] = 0
F[24,x] = F[25,x]*F[5,x]
F[25,x] = F[26,x]+F[27,x]
F[26,x] = F[5,x]
F[27,x] = F[22,x]
F[28,x] = F[17,x]*F[5,x]
F[29,x] = F[23,x]+F[30,x]+F[50,x]
F[30,x] = F[31,x]*F[5,x]
F[31,x] = F[32,x]+F[35,x]
F[32,x] = F[14,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[14,x]*F[5,x]
F[35,x] = F[29,x]+F[36,x]
F[36,x] = 2*F[23,x]+F[37,x]+F[41,x]
F[37,x] = F[38,x]*F[5,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[33,x]
F[40,x] = F[36,x]
F[41,x] = F[42,x]*F[5,x]
F[42,x] = F[43,x]
F[43,x] = F[44,x]*F[5,x]
F[44,x] = F[32,x]+F[45,x]
F[45,x] = F[42,x]+F[46,x]
F[46,x] = 2*F[23,x]+F[41,x]+F[47,x]
F[47,x] = F[48,x]*F[5,x]
F[48,x] = F[39,x]+F[49,x]
F[49,x] = F[46,x]
F[50,x] = F[5,x]*F[51,x]
F[51,x] = F[17,x]+F[42,x]
F[52,x] = F[23,x]+F[53,x]+F[94,x]
F[53,x] = F[5,x]*F[54,x]
F[54,x] = F[55,x]+F[62,x]
F[55,x] = F[3,x]+F[56,x]
F[56,x] = F[23,x]+F[57,x]+F[58,x]
F[57,x] = F[5,x]*F[55,x]
F[58,x] = F[5,x]*F[59,x]
F[59,x] = F[5,x]+F[60,x]
F[60,x] = F[23,x]+F[58,x]+F[61,x]
F[61,x] = F[3,x]*F[5,x]
F[62,x] = F[63,x]+F[99,x]
F[63,x] = F[23,x]+F[64,x]+F[94,x]
F[64,x] = F[5,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[3,x]+F[60,x]
F[67,x] = F[63,x]+F[68,x]
F[68,x] = F[23,x]+F[69,x]+F[73,x]+F[85,x]
F[69,x] = F[5,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[60,x]
F[72,x] = F[68,x]
F[73,x] = F[5,x]*F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[5,x]*F[76,x]
F[76,x] = F[77,x]+F[79,x]
F[77,x] = F[3,x]+F[78,x]
F[78,x] = F[61,x]
F[79,x] = F[74,x]+F[80,x]
F[80,x] = 2*F[23,x]+F[73,x]+F[81,x]
F[81,x] = F[5,x]*F[82,x]
F[82,x] = F[83,x]+F[84,x]
F[83,x] = F[78,x]
F[84,x] = F[80,x]
F[85,x] = F[5,x]*F[86,x]
F[86,x] = F[87,x]+F[89,x]
F[87,x] = F[88,x]
F[88,x] = F[3,x]*F[5,x]
F[89,x] = 2*F[23,x]+F[85,x]+F[90,x]
F[90,x] = F[5,x]*F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[5,x]*F[93,x]
F[93,x] = F[3,x]+F[91,x]
F[94,x] = F[5,x]*F[95,x]
F[95,x] = F[3,x]+F[96,x]
F[96,x] = F[23,x]+F[94,x]+F[97,x]
F[97,x] = F[5,x]*F[98,x]
F[98,x] = F[3,x]+F[96,x]
F[99,x] = F[100,x]+F[124,x]+F[23,x]+F[85,x]
F[100,x] = F[101,x]*F[5,x]
F[101,x] = F[102,x]+F[105,x]
F[102,x] = F[103,x]+F[56,x]
F[103,x] = F[104,x]
F[104,x] = F[5,x]*F[56,x]
F[105,x] = F[106,x]+F[99,x]
F[106,x] = 2*F[23,x]+F[107,x]+F[111,x]+F[123,x]
F[107,x] = F[108,x]*F[5,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[103,x]
F[110,x] = F[106,x]
F[111,x] = F[112,x]*F[5,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]*F[5,x]
F[114,x] = F[115,x]+F[117,x]
F[115,x] = F[116,x]+F[56,x]
F[116,x] = F[104,x]
F[117,x] = F[112,x]+F[118,x]
F[118,x] = 3*F[23,x]+F[111,x]+F[119,x]
F[119,x] = F[120,x]*F[5,x]
F[120,x] = F[121,x]+F[122,x]
F[121,x] = F[116,x]
F[122,x] = F[118,x]
F[123,x] = 0
F[124,x] = F[125,x]*F[5,x]
F[125,x] = F[112,x]+F[74,x]
F[126,x] = F[127,x]
F[127,x] = F[128,x,1]
F[128,x,k[0]] = F[129,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]*F[140,x,k[0]]*F[5,x]
F[131,x,k[0]] = F[132,x,k[0]]+F[150,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]+F[95,x]
F[133,x,k[0]] = F[134,x,k[0]]+F[141,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]*F[5,x]
F[136,x,k[0]] = F[134,x,k[0]]+F[137,x,k[0]]
F[137,x,k[0]] = F[138,x,k[0]]
F[138,x,k[0]] = F[139,x,k[0]]*F[140,x,k[0]]
F[139,x,k[0]] = k[0]*x
F[140,x,k[0]] = F[137,x,k[0]]+F[2,x]
F[141,x,k[0]] = 2*F[23,x]+F[142,x,k[0]]+F[149,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]*F[5,x]
F[143,x,k[0]] = F[141,x,k[0]]+F[144,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]+F[147,x,k[0]]+F[23,x]
F[145,x,k[0]] = F[139,x,k[0]]*F[146,x,k[0]]
F[146,x,k[0]] = F[144,x,k[0]]+F[3,x]
F[147,x,k[0]] = F[148,x,k[0]]*F[5,x]
F[148,x,k[0]] = F[137,x,k[0]]+F[144,x,k[0]]
F[149,x,k[0]] = F[133,x,k[0]]*F[5,x]
F[150,x,k[0]] = (F[129,x,k[0]]*k[0]-F[129,x,1])/(-1+k[0])
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_{126}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{52}\! \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_{16}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{2}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{5}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{29}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{5}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{21}\! \left(x \right) = F_{17}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)+F_{28}\! \left(x \right)
F_{23}\! \left(x \right) = 0
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{5}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)
F_{26}\! \left(x \right) = F_{5}\! \left(x \right)
F_{27}\! \left(x \right) = F_{22}\! \left(x \right)
F_{28}\! \left(x \right) = F_{17}\! \left(x \right) F_{5}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right)+F_{30}\! \left(x \right)+F_{50}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{5}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = F_{14}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{14}\! \left(x \right) F_{5}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{5}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{33}\! \left(x \right)
F_{40}\! \left(x \right) = F_{36}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right) F_{5}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right) F_{5}\! \left(x \right)
F_{44}\! \left(x \right) = F_{32}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{42}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{41}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right) F_{5}\! \left(x \right)
F_{48}\! \left(x \right) = F_{39}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{46}\! \left(x \right)
F_{50}\! \left(x \right) = F_{5}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{17}\! \left(x \right)+F_{42}\! \left(x \right)
F_{52}\! \left(x \right) = F_{23}\! \left(x \right)+F_{53}\! \left(x \right)+F_{94}\! \left(x \right)
F_{53}\! \left(x \right) = F_{5}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{62}\! \left(x \right)
F_{55}\! \left(x \right) = F_{3}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{23}\! \left(x \right)+F_{57}\! \left(x \right)+F_{58}\! \left(x \right)
F_{57}\! \left(x \right) = F_{5}\! \left(x \right) F_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{5}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{5}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{23}\! \left(x \right)+F_{58}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{3}\! \left(x \right) F_{5}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{99}\! \left(x \right)
F_{63}\! \left(x \right) = F_{23}\! \left(x \right)+F_{64}\! \left(x \right)+F_{94}\! \left(x \right)
F_{64}\! \left(x \right) = F_{5}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{3}\! \left(x \right)+F_{60}\! \left(x \right)
F_{67}\! \left(x \right) = F_{63}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{23}\! \left(x \right)+F_{69}\! \left(x \right)+F_{73}\! \left(x \right)+F_{85}\! \left(x \right)
F_{69}\! \left(x \right) = F_{5}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{60}\! \left(x \right)
F_{72}\! \left(x \right) = F_{68}\! \left(x \right)
F_{73}\! \left(x \right) = F_{5}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{5}\! \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_{3}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{61}\! \left(x \right)
F_{79}\! \left(x \right) = F_{74}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{73}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{5}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = F_{78}\! \left(x \right)
F_{84}\! \left(x \right) = F_{80}\! \left(x \right)
F_{85}\! \left(x \right) = F_{5}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{89}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{3}\! \left(x \right) F_{5}\! \left(x \right)
F_{89}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{85}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{5}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{5}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{3}\! \left(x \right)+F_{91}\! \left(x \right)
F_{94}\! \left(x \right) = F_{5}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{3}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{23}\! \left(x \right)+F_{94}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{5}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{3}\! \left(x \right)+F_{96}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{124}\! \left(x \right)+F_{23}\! \left(x \right)+F_{85}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{5}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{105}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{56}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{5}\! \left(x \right) F_{56}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{99}\! \left(x \right)
F_{106}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{107}\! \left(x \right)+F_{111}\! \left(x \right)+F_{123}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{5}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{103}\! \left(x \right)
F_{110}\! \left(x \right) = F_{106}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{5}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{5}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{117}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{56}\! \left(x \right)
F_{116}\! \left(x \right) = F_{104}\! \left(x \right)
F_{117}\! \left(x \right) = F_{112}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = 3 F_{23}\! \left(x \right)+F_{111}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{5}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{122}\! \left(x \right)
F_{121}\! \left(x \right) = F_{116}\! \left(x \right)
F_{122}\! \left(x \right) = F_{118}\! \left(x \right)
F_{123}\! \left(x \right) = 0
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{5}\! \left(x \right)
F_{125}\! \left(x \right) = F_{112}\! \left(x \right)+F_{74}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x , 1\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_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right) F_{140}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right)+F_{150}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{95}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{136}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{137}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right) F_{140}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = y x
F_{140}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{2}\! \left(x \right)
F_{141}\! \left(x , y\right) = 2 F_{23}\! \left(x \right)+F_{142}\! \left(x , y\right)+F_{149}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{143}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{144}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)+F_{147}\! \left(x , y\right)+F_{23}\! \left(x \right)
F_{145}\! \left(x , y\right) = F_{139}\! \left(x , y\right) F_{146}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{3}\! \left(x \right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{148}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{144}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{133}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{150}\! \left(x , y\right) = \frac{F_{129}\! \left(x , y\right) y -F_{129}\! \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_126(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_52(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_16(x))
Eq(F_13(x), F_14(x) + F_2(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_5(x))
Eq(F_16(x), F_17(x) + F_29(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_5(x))
Eq(F_19(x), F_20(x) + F_21(x))
Eq(F_20(x), F_2(x) + F_5(x))
Eq(F_21(x), F_17(x) + F_22(x))
Eq(F_22(x), F_23(x) + F_24(x) + F_28(x))
Eq(F_23(x), 0)
Eq(F_24(x), F_25(x)*F_5(x))
Eq(F_25(x), F_26(x) + F_27(x))
Eq(F_26(x), F_5(x))
Eq(F_27(x), F_22(x))
Eq(F_28(x), F_17(x)*F_5(x))
Eq(F_29(x), F_23(x) + F_30(x) + F_50(x))
Eq(F_30(x), F_31(x)*F_5(x))
Eq(F_31(x), F_32(x) + F_35(x))
Eq(F_32(x), F_14(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_14(x)*F_5(x))
Eq(F_35(x), F_29(x) + F_36(x))
Eq(F_36(x), 2*F_23(x) + F_37(x) + F_41(x))
Eq(F_37(x), F_38(x)*F_5(x))
Eq(F_38(x), F_39(x) + F_40(x))
Eq(F_39(x), F_33(x))
Eq(F_40(x), F_36(x))
Eq(F_41(x), F_42(x)*F_5(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x)*F_5(x))
Eq(F_44(x), F_32(x) + F_45(x))
Eq(F_45(x), F_42(x) + F_46(x))
Eq(F_46(x), 2*F_23(x) + F_41(x) + F_47(x))
Eq(F_47(x), F_48(x)*F_5(x))
Eq(F_48(x), F_39(x) + F_49(x))
Eq(F_49(x), F_46(x))
Eq(F_50(x), F_5(x)*F_51(x))
Eq(F_51(x), F_17(x) + F_42(x))
Eq(F_52(x), F_23(x) + F_53(x) + F_94(x))
Eq(F_53(x), F_5(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_62(x))
Eq(F_55(x), F_3(x) + F_56(x))
Eq(F_56(x), F_23(x) + F_57(x) + F_58(x))
Eq(F_57(x), F_5(x)*F_55(x))
Eq(F_58(x), F_5(x)*F_59(x))
Eq(F_59(x), F_5(x) + F_60(x))
Eq(F_60(x), F_23(x) + F_58(x) + F_61(x))
Eq(F_61(x), F_3(x)*F_5(x))
Eq(F_62(x), F_63(x) + F_99(x))
Eq(F_63(x), F_23(x) + F_64(x) + F_94(x))
Eq(F_64(x), F_5(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_3(x) + F_60(x))
Eq(F_67(x), F_63(x) + F_68(x))
Eq(F_68(x), F_23(x) + F_69(x) + F_73(x) + F_85(x))
Eq(F_69(x), F_5(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_60(x))
Eq(F_72(x), F_68(x))
Eq(F_73(x), F_5(x)*F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_5(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_79(x))
Eq(F_77(x), F_3(x) + F_78(x))
Eq(F_78(x), F_61(x))
Eq(F_79(x), F_74(x) + F_80(x))
Eq(F_80(x), 2*F_23(x) + F_73(x) + F_81(x))
Eq(F_81(x), F_5(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_84(x))
Eq(F_83(x), F_78(x))
Eq(F_84(x), F_80(x))
Eq(F_85(x), F_5(x)*F_86(x))
Eq(F_86(x), F_87(x) + F_89(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_3(x)*F_5(x))
Eq(F_89(x), 2*F_23(x) + F_85(x) + F_90(x))
Eq(F_90(x), F_5(x)*F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_5(x)*F_93(x))
Eq(F_93(x), F_3(x) + F_91(x))
Eq(F_94(x), F_5(x)*F_95(x))
Eq(F_95(x), F_3(x) + F_96(x))
Eq(F_96(x), F_23(x) + F_94(x) + F_97(x))
Eq(F_97(x), F_5(x)*F_98(x))
Eq(F_98(x), F_3(x) + F_96(x))
Eq(F_99(x), F_100(x) + F_124(x) + F_23(x) + F_85(x))
Eq(F_100(x), F_101(x)*F_5(x))
Eq(F_101(x), F_102(x) + F_105(x))
Eq(F_102(x), F_103(x) + F_56(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_5(x)*F_56(x))
Eq(F_105(x), F_106(x) + F_99(x))
Eq(F_106(x), F_107(x) + F_111(x) + F_123(x) + 2*F_23(x))
Eq(F_107(x), F_108(x)*F_5(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_103(x))
Eq(F_110(x), F_106(x))
Eq(F_111(x), F_112(x)*F_5(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x)*F_5(x))
Eq(F_114(x), F_115(x) + F_117(x))
Eq(F_115(x), F_116(x) + F_56(x))
Eq(F_116(x), F_104(x))
Eq(F_117(x), F_112(x) + F_118(x))
Eq(F_118(x), F_111(x) + F_119(x) + 3*F_23(x))
Eq(F_119(x), F_120(x)*F_5(x))
Eq(F_120(x), F_121(x) + F_122(x))
Eq(F_121(x), F_116(x))
Eq(F_122(x), F_118(x))
Eq(F_123(x), 0)
Eq(F_124(x), F_125(x)*F_5(x))
Eq(F_125(x), F_112(x) + F_74(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x, 1))
Eq(F_128(x, k_0), F_129(x, k_0))
Eq(F_129(x, k_0), F_130(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0)*F_140(x, k_0)*F_5(x))
Eq(F_131(x, k_0), F_132(x, k_0) + F_150(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0) + F_95(x))
Eq(F_133(x, k_0), F_134(x, k_0) + F_141(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0)*F_5(x))
Eq(F_136(x, k_0), F_134(x, k_0) + F_137(x, k_0))
Eq(F_137(x, k_0), F_138(x, k_0))
Eq(F_138(x, k_0), F_139(x, k_0)*F_140(x, k_0))
Eq(F_139(x, k_0), k_0*x)
Eq(F_140(x, k_0), F_137(x, k_0) + F_2(x))
Eq(F_141(x, k_0), F_142(x, k_0) + F_149(x, k_0) + 2*F_23(x))
Eq(F_142(x, k_0), F_143(x, k_0)*F_5(x))
Eq(F_143(x, k_0), F_141(x, k_0) + F_144(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0) + F_147(x, k_0) + F_23(x))
Eq(F_145(x, k_0), F_139(x, k_0)*F_146(x, k_0))
Eq(F_146(x, k_0), F_144(x, k_0) + F_3(x))
Eq(F_147(x, k_0), F_148(x, k_0)*F_5(x))
Eq(F_148(x, k_0), F_137(x, k_0) + F_144(x, k_0))
Eq(F_149(x, k_0), F_133(x, k_0)*F_5(x))
Eq(F_150(x, k_0), (-k_0*F_129(x, k_0) + F_129(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, 1, 3], "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, 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, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "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, 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, 1], "pos": [[0, 0], [0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "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, 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, 1], "pos": [[0, 0], [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": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, 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