0132_1203_2130_3012
Counting sequence:
1, 1, 2, 6, 20, 59, 151, 352, 774, 1643, 3415, 7010, 14282, 28963, 58557, 118138, 237962, 478717, 962065, 1931794, 3876232, 7773253, 15580577, 31216836, 62524460, 125196669, 250633431, 501656572, 1003945164, 2008914663, 4019488715, 8041664660, 16087679962, 32182402383, 64376203067, 128770852758, 257571557022, 515191419527, 1030461004225, 2061048488174, 4122301631262, 8244934408193, 16490404629077, 32981676229766, 65964755258300, 131931780302729, 263867233207461, 527740408821592, 1055490432671904, 2110996422800833, 4222018018110715, 8444076766212560, 16888219434952192, 33776545502451403, 67553263540007727, 135106806247700328, 270214064198225582, 540428859266998387, 1080858901107408735, 2161719715658818954, 4323442527335096242, 8646890064131699883, 17293788233742415877, 34587589582425408546, 69175200385270466290, 138350435105901217989, 276700925767582433241, 553401941426305215162, 1106804028299530845744, 2213608291937122528653, 4427216964659226386665, 8854434545441495020460, 17708870087791013701972, 35417741788613093400773, 70835486187165276552287, 141670976597300708949348, 283341960027510663595892, 566683931110900728840047, 1133367880110590105136595, 2266735789165848259493884, 4533471625165153215785922, 9066943326108431177716823, 18133886774828443798508227, 36267773748046593786372926, 72535547817094475205319430, 145071096153579944232717199, 290142193147552169920240521, 580284387654887615117525782, 1160568777509950786967068934, 2321137558579860405943372873, 4642275122919855200628177565, 9284550255159803622007208110, 18569100525399834853506894052, 37138201075199990537257318993, 74276402189880529514250853997, 148552804443641928298481669568, 297105608990645274306679738952, 594211218148532835593056069257, 1188422436567669375875525367555, 2376844873573184743420160801464, 4753689747854819183198845152552
Generating function in Maple syntax:
(x^8+7*x^7-6*x^6+x^5+3*x^4-13*x^3+14*x^2-6*x+1)/(2*x-1)/(x^2+x-1)/(-1+x)^4
Generating function in latex syntax:
\frac{x^{8}+7 x^{7}-6 x^{6}+x^{5}+3 x^{4}-13 x^{3}+14 x^{2}-6 x +1}{\left(2 x -1\right) \left(x^{2}+x -1\right) \left(-1+x \right)^{4}}
Generating function in sympy syntax:
(x**8 + 7*x**7 - 6*x**6 + x**5 + 3*x**4 - 13*x**3 + 14*x**2 - 6*x + 1)/((x - 1)**4*(2*x - 1)*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
-(2*x-1)*(x^2+x-1)*(-1+x)^4*F(x)+x^8+7*x^7-6*x^6+x^5+3*x^4-13*x^3+14*x^2-6*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right) \left(x^{2}+x -1\right) \left(-1+x \right)^{4} F \! \left(x \right)+x^{8}+7 x^{7}-6 x^{6}+x^{5}+3 x^{4}-13 x^{3}+14 x^{2}-6 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/60*(48*5^(1/2)-120)*(-1/2*5^(1/2)-1/2)^(-n)+1/60*(-48*5^(1/2)-120)*(1/2*5^(1/2)-1/2)^(-n)+1/3*n^3-7/2*n^2+37/6*n+15/4*2^n-4)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{\left(48 \sqrt{5}-120\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{60}+\frac{\left(-48 \sqrt{5}-120\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{60}+\frac{n^{3}}{3}-\\\frac{7 n^{2}}{2}+\frac{37 n}{6}+\frac{15 \,2^{n}}{4}-4 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 59
a(6) = 151
a(7) = 352
a(8) = 774
a(n+3) = 1/3*n^3-11/2*n^2-2*a(n)-a(n+1)+3*a(n+2)+109/6*n-8, n >= 9
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) = 59
a \! \left(6\right) = 151
a \! \left(7\right) = 352
a \! \left(8\right) = 774
a \! \left(n +3\right) = \frac{n^{3}}{3}-\frac{11 n^{2}}{2}-2 a \! \left(n \right)-a \! \left(n +1\right)+3 a \! \left(n +2\right)+\frac{109 n}{6}-8, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15592/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[42,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[26,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[4,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]+F[21,x]+F[25,x]
F[20,x] = 0
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[4,x]
F[24,x] = F[21,x]
F[25,x] = F[14,x]*F[4,x]
F[26,x] = F[20,x]+F[27,x]+F[39,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[11,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[11,x]*F[4,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[27,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[30,x]
F[38,x] = F[35,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[14,x]+F[41,x]
F[41,x] = F[39,x]
F[42,x] = F[43,x]+F[73,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[49,x]
F[46,x] = F[1,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[46,x]
F[49,x] = F[43,x]+F[50,x]
F[50,x] = F[20,x]+F[51,x]+F[72,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[53,x]+F[57,x]
F[53,x] = F[47,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[47,x]+F[54,x]
F[57,x] = F[58,x]+F[63,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[47,x]
F[62,x] = F[58,x]
F[63,x] = F[64,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[54,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[54,x]
F[71,x] = F[68,x]
F[72,x] = F[4,x]*F[49,x]
F[73,x] = F[128,x]+F[20,x]+F[74,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[103,x]+F[76,x]
F[76,x] = F[7,x]+F[77,x]
F[77,x] = F[20,x]+F[78,x]+F[81,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[11,x]+F[80,x]
F[80,x] = F[78,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[83,x]+F[86,x]
F[83,x] = F[47,x]+F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[4,x]*F[83,x]
F[86,x] = F[87,x]+F[99,x]
F[87,x] = F[20,x]+F[88,x]+F[91,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[4,x]+F[90,x]
F[90,x] = F[88,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[93,x]+F[96,x]
F[93,x] = F[47,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[4,x]*F[47,x]
F[96,x] = F[87,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[4,x]*F[87,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[4,x]
F[101,x] = F[102,x]+F[87,x]
F[102,x] = F[100,x]
F[103,x] = F[104,x]+F[119,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[4,x]
F[106,x] = F[107,x]+F[109,x]
F[107,x] = F[108,x]+F[7,x]
F[108,x] = F[78,x]
F[109,x] = F[104,x]+F[110,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]*F[4,x]
F[112,x] = F[113,x]+F[114,x]
F[113,x] = F[108,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[4,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[108,x]
F[118,x] = F[115,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[123,x]
F[122,x] = F[77,x]
F[123,x] = F[124,x]
F[124,x] = F[125,x]*F[4,x]
F[125,x] = F[126,x]+F[127,x]
F[126,x] = F[77,x]
F[127,x] = F[124,x]
F[128,x] = F[129,x]*F[4,x]
F[129,x] = F[130,x]+F[133,x]
F[130,x] = F[131,x]+F[43,x]
F[131,x] = F[132,x]
F[132,x] = F[130,x]*F[4,x]
F[133,x] = F[134,x]+F[143,x]
F[134,x] = F[135,x]+F[20,x]+F[51,x]
F[135,x] = F[136,x]*F[4,x]
F[136,x] = F[137,x]+F[140,x]
F[137,x] = F[138,x]+F[43,x]
F[138,x] = F[139,x]
F[139,x] = F[4,x]*F[43,x]
F[140,x] = F[134,x]+F[141,x]
F[141,x] = F[142,x]
F[142,x] = F[134,x]*F[4,x]
F[143,x] = F[144,x]
F[144,x] = F[145,x]*F[4,x]
F[145,x] = F[134,x]+F[146,x]
F[146,x] = F[144,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{42}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{26}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{21}\! \left(x \right)
F_{25}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{20}\! \left(x \right)+F_{27}\! \left(x \right)+F_{39}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{27}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \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_{35}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{14}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{73}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \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_{1}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{49}\! \left(x \right) = F_{43}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{20}\! \left(x \right)+F_{51}\! \left(x \right)+F_{72}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{57}\! \left(x \right)
F_{53}\! \left(x \right) = F_{47}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{47}\! \left(x \right)+F_{54}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{63}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{47}\! \left(x \right)
F_{62}\! \left(x \right) = F_{58}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \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_{54}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{54}\! \left(x \right)
F_{71}\! \left(x \right) = F_{68}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{73}\! \left(x \right) = F_{128}\! \left(x \right)+F_{20}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{103}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{7}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{20}\! \left(x \right)+F_{78}\! \left(x \right)+F_{81}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{11}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{78}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{86}\! \left(x \right)
F_{83}\! \left(x \right) = F_{47}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{99}\! \left(x \right)
F_{87}\! \left(x \right) = F_{20}\! \left(x \right)+F_{88}\! \left(x \right)+F_{91}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{88}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{96}\! \left(x \right)
F_{93}\! \left(x \right) = F_{47}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{96}\! \left(x \right) = F_{87}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{87}\! \left(x \right)
F_{102}\! \left(x \right) = F_{100}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{119}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{109}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{7}\! \left(x \right)
F_{108}\! \left(x \right) = F_{78}\! \left(x \right)
F_{109}\! \left(x \right) = F_{104}\! \left(x \right)+F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{4}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{114}\! \left(x \right)
F_{113}\! \left(x \right) = F_{108}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{4}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{108}\! \left(x \right)
F_{118}\! \left(x \right) = F_{115}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{123}\! \left(x \right)
F_{122}\! \left(x \right) = F_{77}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{4}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{127}\! \left(x \right)
F_{126}\! \left(x \right) = F_{77}\! \left(x \right)
F_{127}\! \left(x \right) = F_{124}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{4}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{133}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{43}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{130}\! \left(x \right) F_{4}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{143}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{20}\! \left(x \right)+F_{51}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{140}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{43}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{140}\! \left(x \right) = F_{134}\! \left(x \right)+F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{134}\! \left(x \right) F_{4}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right) F_{4}\! \left(x \right)
F_{145}\! \left(x \right) = F_{134}\! \left(x \right)+F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{144}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_42(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_26(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_4(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_25(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_4(x))
Eq(F_24(x), F_21(x))
Eq(F_25(x), F_14(x)*F_4(x))
Eq(F_26(x), F_20(x) + F_27(x) + F_39(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_11(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_11(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_27(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_30(x))
Eq(F_38(x), F_35(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_14(x) + F_41(x))
Eq(F_41(x), F_39(x))
Eq(F_42(x), F_43(x) + F_73(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_49(x))
Eq(F_46(x), F_1(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_4(x)*F_46(x))
Eq(F_49(x), F_43(x) + F_50(x))
Eq(F_50(x), F_20(x) + F_51(x) + F_72(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_57(x))
Eq(F_53(x), F_47(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_47(x) + F_54(x))
Eq(F_57(x), F_58(x) + F_63(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_47(x))
Eq(F_62(x), F_58(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_54(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_54(x))
Eq(F_71(x), F_68(x))
Eq(F_72(x), F_4(x)*F_49(x))
Eq(F_73(x), F_128(x) + F_20(x) + F_74(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_103(x) + F_76(x))
Eq(F_76(x), F_7(x) + F_77(x))
Eq(F_77(x), F_20(x) + F_78(x) + F_81(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_11(x) + F_80(x))
Eq(F_80(x), F_78(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_86(x))
Eq(F_83(x), F_47(x) + F_84(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_4(x)*F_83(x))
Eq(F_86(x), F_87(x) + F_99(x))
Eq(F_87(x), F_20(x) + F_88(x) + F_91(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_4(x) + F_90(x))
Eq(F_90(x), F_88(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_96(x))
Eq(F_93(x), F_47(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_4(x)*F_47(x))
Eq(F_96(x), F_87(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_4(x)*F_87(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_4(x))
Eq(F_101(x), F_102(x) + F_87(x))
Eq(F_102(x), F_100(x))
Eq(F_103(x), F_104(x) + F_119(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_4(x))
Eq(F_106(x), F_107(x) + F_109(x))
Eq(F_107(x), F_108(x) + F_7(x))
Eq(F_108(x), F_78(x))
Eq(F_109(x), F_104(x) + F_110(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x)*F_4(x))
Eq(F_112(x), F_113(x) + F_114(x))
Eq(F_113(x), F_108(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_4(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_108(x))
Eq(F_118(x), F_115(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x)*F_4(x))
Eq(F_121(x), F_122(x) + F_123(x))
Eq(F_122(x), F_77(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_125(x)*F_4(x))
Eq(F_125(x), F_126(x) + F_127(x))
Eq(F_126(x), F_77(x))
Eq(F_127(x), F_124(x))
Eq(F_128(x), F_129(x)*F_4(x))
Eq(F_129(x), F_130(x) + F_133(x))
Eq(F_130(x), F_131(x) + F_43(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_130(x)*F_4(x))
Eq(F_133(x), F_134(x) + F_143(x))
Eq(F_134(x), F_135(x) + F_20(x) + F_51(x))
Eq(F_135(x), F_136(x)*F_4(x))
Eq(F_136(x), F_137(x) + F_140(x))
Eq(F_137(x), F_138(x) + F_43(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_4(x)*F_43(x))
Eq(F_140(x), F_134(x) + F_141(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_134(x)*F_4(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_145(x)*F_4(x))
Eq(F_145(x), F_134(x) + F_146(x))
Eq(F_146(x), F_144(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": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 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": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": 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