0123_0231_1302_1320_3021
Counting sequence:
1, 1, 2, 6, 19, 53, 134, 329, 808, 2004, 5024, 12708, 32365, 82858, 212987, 549265, 1420255, 3680525, 9555488, 24846335, 64688218, 168595290, 439786442, 1148010978, 2998478719, 7835365888, 20482452389, 53559561679, 140087179873, 366475484579, 958869510794, 2509159968173, 6566597126620, 17186470660848, 44984224919972, 117748487357520, 308224729929025, 806850540500230, 2112172272747263, 5529348450159805, 14475220242701203, 37894972248145385, 99206947722663332, 259720235922749963, 679942215173492494, 1780082770097727798, 4660257716608066094, 12200591423679967854, 31941314244292323763, 83622937892824956604, 218926655009252410889, 573155303100699919963, 1500535735855638462325, 3928444726854309341663, 10284783808008500604782, 26925876860823661139225, 70492785975867513307120, 184552357217789126089260, 483164033475920732208488, 1264939229799615550295100, 3311652611087812368717013, 8670016477764797436976930, 22698392498750937666532547, 59425152227461542935407273, 155577046313350369733555719, 407305950395562171149574533, 1066340731086359848876955624, 2791716092983721776591179479, 7308807243493528264688974978, 19134705019530936548205759954, 50095306560720684367678788434, 131151212116980434382912475578, 343358324625132278142384178855, 898923751280665766177214735928, 2353412907966215847475856559917, 6161314929526387620064842361255, 16130531793249167079630234062665, 42230280273132370511214164305115, 110560308667248091755919222603538, 289450645001367466394618140587845, 757791624863475964772605892478148, 1983924226604524810749583761781800, 5193981048905469369402999519327212, 13598018907871509373861294402290408, 35600075649926079450080985606057769, 93202207991736307462374551665566718, 244006548223733074089413818715313479, 638817436473945525471379944780313429, 1672445760782233020377293579526691643, 4378519845031341165208718888204252129, 11463113772609622921231465207099757804, 30010821469354506864223212843531820643, 78569350628490484950457909277188118710, 205697230402035380040279314361054985518, 538522340549143034266816287483296968502, 1409869791187829510933399365306026631110, 3691087032897979134840556062594265235035, 9663391307270899286124046570245935458420, 25299086888439349748445997622582277424913, 66233869357086508488728491204179176404915, 173402521180879085736139999718913424992733
Generating function in Maple syntax:
(2*x^10-14*x^9+25*x^8-x^7-20*x^6+36*x^5-62*x^4+62*x^3-33*x^2+9*x-1)/(x^2-3*x+1)/(2*x-1)^2/(x-1)^3
Generating function in latex syntax:
\frac{2 x^{10}-14 x^{9}+25 x^{8}-x^{7}-20 x^{6}+36 x^{5}-62 x^{4}+62 x^{3}-33 x^{2}+9 x -1}{\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{3}}
Generating function in sympy syntax:
(2*x**10 - 14*x**9 + 25*x**8 - x**7 - 20*x**6 + 36*x**5 - 62*x**4 + 62*x**3 - 33*x**2 + 9*x - 1)/((x - 1)**3*(2*x - 1)**2*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
-(x^2-3*x+1)*(2*x-1)^2*(x-1)^3*F(x)+2*x^10-14*x^9+25*x^8-x^7-20*x^6+36*x^5-62*x^4+62*x^3-33*x^2+9*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{3} F \! \left(x \right)+2 x^{10}-14 x^{9}+25 x^{8}-x^{7}-20 x^{6}+36 x^{5}-62 x^{4}+62 x^{3}-33 x^{2}+9 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 3,6,1/80*(-8*5^(1/2)+40)*(3/2-1/2*5^(1/2))^(-n)+1/80*(8*5^(1/2)+40)*(3/2+1/2*5^(1/2))^(-n)+1/80*(5*n+10)*2^n+3/2*n^2-17/2*n+10)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 6 & n =3 \\ \frac{\left(-8 \sqrt{5}+40\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{80}+\frac{\left(8 \sqrt{5}+40\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{80}+\frac{\left(5 n +10\right) 2^{n}}{80}\\+\frac{3 n^{2}}{2}-\frac{17 n}{2}+10 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 53
a(6) = 134
a(7) = 329
a(8) = 808
a(9) = 2004
a(10) = 5024
a(n+4) = -3/2*n^2-4*a(n)+16*a(n+1)-17*a(n+2)+7*a(n+3)+23/2*n-11, n >= 11
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 53
a \! \left(6\right) = 134
a \! \left(7\right) = 329
a \! \left(8\right) = 808
a \! \left(9\right) = 2004
a \! \left(10\right) = 5024
a \! \left(n +4\right) = -\frac{3 n^{2}}{2}-4 a \! \left(n \right)+16 a \! \left(n +1\right)-17 a \! \left(n +2\right)+7 a \! \left(n +3\right)+\frac{23 n}{2}-11, \quad n \geq 11
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/17444/
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[29,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[24,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[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[4,x]
F[23,x] = F[19,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[11,x]
F[28,x] = F[24,x]
F[29,x] = F[30,x]+F[66,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[36,x]
F[33,x] = F[1,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[17,x]*F[4,x]
F[36,x] = F[30,x]+F[37,x]
F[37,x] = F[38,x]+F[39,x]+F[64,x]
F[38,x] = 0
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[34,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[22,x]*F[4,x]
F[44,x] = F[37,x]+F[45,x]
F[45,x] = 2*F[38,x]+F[46,x]+F[50,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = F[42,x]
F[49,x] = F[45,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[38,x]+F[53,x]+F[63,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[57,x]
F[55,x] = F[4,x]+F[56,x]
F[56,x] = F[43,x]
F[57,x] = F[52,x]+F[58,x]
F[58,x] = 2*F[38,x]+F[50,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[56,x]
F[62,x] = F[58,x]
F[63,x] = F[30,x]*F[4,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[30,x]+F[52,x]
F[66,x] = F[136,x]+F[38,x]+F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[81,x]
F[69,x] = F[7,x]+F[70,x]
F[70,x] = F[38,x]+F[71,x]+F[76,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[11,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[4,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[34,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[27,x]*F[4,x]
F[81,x] = F[66,x]+F[82,x]
F[82,x] = F[110,x]+F[135,x]+F[38,x]+F[83,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[85,x]+F[89,x]
F[85,x] = F[70,x]+F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[73,x]
F[89,x] = F[82,x]+F[90,x]
F[90,x] = 2*F[38,x]+F[109,x]+F[91,x]+F[95,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[93,x]+F[94,x]
F[93,x] = F[86,x]
F[94,x] = F[90,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[102,x]
F[100,x] = F[101,x]+F[73,x]
F[101,x] = F[87,x]
F[102,x] = F[103,x]+F[97,x]
F[103,x] = 2*F[38,x]+F[104,x]+F[108,x]+F[95,x]
F[104,x] = F[105,x]*F[4,x]
F[105,x] = F[106,x]+F[107,x]
F[106,x] = F[101,x]
F[107,x] = F[103,x]
F[108,x] = 0
F[109,x] = 0
F[110,x] = F[111,x]*F[4,x]
F[111,x] = F[112,x]+F[97,x]
F[112,x] = F[113,x]+F[133,x]+F[38,x]
F[113,x] = F[114,x]*F[4,x]
F[114,x] = F[115,x]+F[119,x]
F[115,x] = F[11,x]+F[116,x]
F[116,x] = F[117,x]+F[38,x]+F[71,x]
F[117,x] = F[118,x]*F[4,x]
F[118,x] = F[34,x]
F[119,x] = F[112,x]+F[120,x]
F[120,x] = F[110,x]+F[121,x]+F[132,x]+F[38,x]
F[121,x] = F[122,x]*F[4,x]
F[122,x] = F[123,x]+F[125,x]
F[123,x] = F[116,x]+F[124,x]
F[124,x] = F[87,x]
F[125,x] = F[120,x]+F[126,x]
F[126,x] = 2*F[38,x]+F[127,x]+F[131,x]+F[95,x]
F[127,x] = F[128,x]*F[4,x]
F[128,x] = F[129,x]+F[130,x]
F[129,x] = F[124,x]
F[130,x] = F[126,x]
F[131,x] = 0
F[132,x] = 0
F[133,x] = F[134,x]*F[4,x]
F[134,x] = F[30,x]
F[135,x] = 0
F[136,x] = F[137,x]*F[4,x]
F[137,x] = F[138,x]
F[138,x] = F[112,x]+F[30,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_{29}\! \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_{24}\! \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_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right)
F_{28}\! \left(x \right) = F_{24}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{66}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{36}\! \left(x \right)
F_{33}\! \left(x \right) = F_{1}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)+F_{64}\! \left(x \right)
F_{38}\! \left(x \right) = 0
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \left(x \right) = F_{34}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{44}\! \left(x \right) = F_{37}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{46}\! \left(x \right)+F_{50}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{42}\! \left(x \right)
F_{49}\! \left(x \right) = F_{45}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{38}\! \left(x \right)+F_{53}\! \left(x \right)+F_{63}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{43}\! \left(x \right)
F_{57}\! \left(x \right) = F_{52}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{50}\! \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_{56}\! \left(x \right)
F_{62}\! \left(x \right) = F_{58}\! \left(x \right)
F_{63}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{30}\! \left(x \right)+F_{52}\! \left(x \right)
F_{66}\! \left(x \right) = F_{136}\! \left(x \right)+F_{38}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{81}\! \left(x \right)
F_{69}\! \left(x \right) = F_{7}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{38}\! \left(x \right)+F_{71}\! \left(x \right)+F_{76}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{11}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \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_{4}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{34}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{81}\! \left(x \right) = F_{66}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{110}\! \left(x \right)+F_{135}\! \left(x \right)+F_{38}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{89}\! \left(x \right)
F_{85}\! \left(x \right) = F_{70}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{73}\! \left(x \right)
F_{89}\! \left(x \right) = F_{82}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{109}\! \left(x \right)+F_{91}\! \left(x \right)+F_{95}\! \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_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{86}\! \left(x \right)
F_{94}\! \left(x \right) = F_{90}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \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_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{102}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{73}\! \left(x \right)
F_{101}\! \left(x \right) = F_{87}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{97}\! \left(x \right)
F_{103}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{104}\! \left(x \right)+F_{108}\! \left(x \right)+F_{95}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{4}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{107}\! \left(x \right)
F_{106}\! \left(x \right) = F_{101}\! \left(x \right)
F_{107}\! \left(x \right) = F_{103}\! \left(x \right)
F_{108}\! \left(x \right) = 0
F_{109}\! \left(x \right) = 0
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{4}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{97}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{133}\! \left(x \right)+F_{38}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{4}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{119}\! \left(x \right)
F_{115}\! \left(x \right) = F_{11}\! \left(x \right)+F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{38}\! \left(x \right)+F_{71}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{4}\! \left(x \right)
F_{118}\! \left(x \right) = F_{34}\! \left(x \right)
F_{119}\! \left(x \right) = F_{112}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{110}\! \left(x \right)+F_{121}\! \left(x \right)+F_{132}\! \left(x \right)+F_{38}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{4}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{125}\! \left(x \right)
F_{123}\! \left(x \right) = F_{116}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{87}\! \left(x \right)
F_{125}\! \left(x \right) = F_{120}\! \left(x \right)+F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{127}\! \left(x \right)+F_{131}\! \left(x \right)+F_{95}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{4}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{130}\! \left(x \right)
F_{129}\! \left(x \right) = F_{124}\! \left(x \right)
F_{130}\! \left(x \right) = F_{126}\! \left(x \right)
F_{131}\! \left(x \right) = 0
F_{132}\! \left(x \right) = 0
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{4}\! \left(x \right)
F_{134}\! \left(x \right) = F_{30}\! \left(x \right)
F_{135}\! \left(x \right) = 0
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{4}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{112}\! \left(x \right)+F_{30}\! \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_29(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_24(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))
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_4(x))
Eq(F_23(x), F_19(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_11(x))
Eq(F_28(x), F_24(x))
Eq(F_29(x), F_30(x) + F_66(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_36(x))
Eq(F_33(x), F_1(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_17(x)*F_4(x))
Eq(F_36(x), F_30(x) + F_37(x))
Eq(F_37(x), F_38(x) + F_39(x) + F_64(x))
Eq(F_38(x), 0)
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_34(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_22(x)*F_4(x))
Eq(F_44(x), F_37(x) + F_45(x))
Eq(F_45(x), 2*F_38(x) + F_46(x) + F_50(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_49(x))
Eq(F_48(x), F_42(x))
Eq(F_49(x), F_45(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_38(x) + F_53(x) + F_63(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_57(x))
Eq(F_55(x), F_4(x) + F_56(x))
Eq(F_56(x), F_43(x))
Eq(F_57(x), F_52(x) + F_58(x))
Eq(F_58(x), 2*F_38(x) + F_50(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_56(x))
Eq(F_62(x), F_58(x))
Eq(F_63(x), F_30(x)*F_4(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_30(x) + F_52(x))
Eq(F_66(x), F_136(x) + F_38(x) + F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_81(x))
Eq(F_69(x), F_7(x) + F_70(x))
Eq(F_70(x), F_38(x) + F_71(x) + F_76(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_11(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_4(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_34(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_27(x)*F_4(x))
Eq(F_81(x), F_66(x) + F_82(x))
Eq(F_82(x), F_110(x) + F_135(x) + F_38(x) + F_83(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_89(x))
Eq(F_85(x), F_70(x) + F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_73(x))
Eq(F_89(x), F_82(x) + F_90(x))
Eq(F_90(x), F_109(x) + 2*F_38(x) + F_91(x) + F_95(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_94(x))
Eq(F_93(x), F_86(x))
Eq(F_94(x), F_90(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_102(x))
Eq(F_100(x), F_101(x) + F_73(x))
Eq(F_101(x), F_87(x))
Eq(F_102(x), F_103(x) + F_97(x))
Eq(F_103(x), F_104(x) + F_108(x) + 2*F_38(x) + F_95(x))
Eq(F_104(x), F_105(x)*F_4(x))
Eq(F_105(x), F_106(x) + F_107(x))
Eq(F_106(x), F_101(x))
Eq(F_107(x), F_103(x))
Eq(F_108(x), 0)
Eq(F_109(x), 0)
Eq(F_110(x), F_111(x)*F_4(x))
Eq(F_111(x), F_112(x) + F_97(x))
Eq(F_112(x), F_113(x) + F_133(x) + F_38(x))
Eq(F_113(x), F_114(x)*F_4(x))
Eq(F_114(x), F_115(x) + F_119(x))
Eq(F_115(x), F_11(x) + F_116(x))
Eq(F_116(x), F_117(x) + F_38(x) + F_71(x))
Eq(F_117(x), F_118(x)*F_4(x))
Eq(F_118(x), F_34(x))
Eq(F_119(x), F_112(x) + F_120(x))
Eq(F_120(x), F_110(x) + F_121(x) + F_132(x) + F_38(x))
Eq(F_121(x), F_122(x)*F_4(x))
Eq(F_122(x), F_123(x) + F_125(x))
Eq(F_123(x), F_116(x) + F_124(x))
Eq(F_124(x), F_87(x))
Eq(F_125(x), F_120(x) + F_126(x))
Eq(F_126(x), F_127(x) + F_131(x) + 2*F_38(x) + F_95(x))
Eq(F_127(x), F_128(x)*F_4(x))
Eq(F_128(x), F_129(x) + F_130(x))
Eq(F_129(x), F_124(x))
Eq(F_130(x), F_126(x))
Eq(F_131(x), 0)
Eq(F_132(x), 0)
Eq(F_133(x), F_134(x)*F_4(x))
Eq(F_134(x), F_30(x))
Eq(F_135(x), 0)
Eq(F_136(x), F_137(x)*F_4(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_112(x) + F_30(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, 2, 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, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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, 2, 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, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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, 2, 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, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], 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