0123_0213_1302_1320_3021
Counting sequence:
1, 1, 2, 6, 19, 53, 135, 333, 820, 2034, 5090, 12841, 32617, 83315, 213790, 550644, 1422584, 3684411, 9561915, 24856897, 64705496, 168623462, 439832270, 1148085405, 2998599453, 7835561583, 20482769410, 53560075048, 140088010980, 366476829839, 958871688015, 2509163491581, 6566602828252, 17186479886970, 44984239848890, 117748511513809, 308224769015569, 806850603744491, 2112172375079590, 5529348615738012, 14475220510613456, 37894972681637667, 99206948424069795, 259720237057650745, 679942217009801888, 1780082773068940238, 4660257721415590310, 12200591431458707013, 31941314256878589765, 83622937913189964519, 218926655042203687690, 573155303154016207696, 1500535735941906030012, 3928444726993893200375, 10284783808234352034615, 26925876861189096431349, 70492785976458800032804, 184552357218745848110946, 483164033477468740959890, 1264939229802120281072377, 3311652611091865108250041, 8670016477771354907291747, 22698392498761547876385070, 59425152227478710615579460, 155577046313378147623585448, 407305950395607116719781643, 1066340731086432572337197835, 2791716092983839445621634353, 7308807243493718657179677800, 19134705019531244609726923574, 50095306560721182821690660990, 131151212116981240898445518061, 343358324625133583111929100397, 898923751280667877662292706655, 2353412907966219263930479459090, 6161314929526393148004543238264, 16130531793249176024024557846164, 42230280273132384983548188973151, 110560308667248115172647571062815, 289450645001367504283680513723117, 757791624863476026078396614080876, 1983924226604524909944436856528202, 5193981048905469529903643335684970, 13598018907871509633556791313403425, 35600075649926079870277126333537633, 93202207991736308142266189304168923, 244006548223733075189501597081405110, 638817436473945527251359360785017068, 1672445760782233023257360773897496960, 4378519845031341169868765498579771379, 11463113772609622928771579011846092915, 30010821469354506876423373258653685801, 78569350628490484970198183497056330032, 205697230402035380072219748996045073310, 538522340549143034318496996338155279190, 1409869791187829511017020508795875041429, 3691087032897979134975857914938971968149, 9663391307270899286342969566080490614231, 25299086888439349748800222470761539326490, 66233869357086508489301639048192993475232, 173402521180879085737067372411106503977836
Generating function in Maple syntax:
(4*x^12-6*x^11-17*x^10+6*x^9+22*x^8-6*x^7+4*x^6-x^5-37*x^4+54*x^3-32*x^2+9*x-1)/(x^2-3*x+1)/(x^2+x-1)/(2*x-1)^2/(x-1)^2
Generating function in latex syntax:
\frac{4 x^{12}-6 x^{11}-17 x^{10}+6 x^{9}+22 x^{8}-6 x^{7}+4 x^{6}-x^{5}-37 x^{4}+54 x^{3}-32 x^{2}+9 x -1}{\left(x^{2}-3 x +1\right) \left(x^{2}+x -1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{2}}
Generating function in sympy syntax:
(4*x**12 - 6*x**11 - 17*x**10 + 6*x**9 + 22*x**8 - 6*x**7 + 4*x**6 - x**5 - 37*x**4 + 54*x**3 - 32*x**2 + 9*x - 1)/((x - 1)**2*(2*x - 1)**2*(x**2 - 3*x + 1)*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
-(x^2-3*x+1)*(x^2+x-1)*(2*x-1)^2*(x-1)^2*F(x)+4*x^12-6*x^11-17*x^10+6*x^9+22*x^8-6*x^7+4*x^6-x^5-37*x^4+54*x^3-32*x^2+9*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{2}-3 x +1\right) \left(x^{2}+x -1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{2} F \! \left(x \right)+4 x^{12}-6 x^{11}-17 x^{10}+6 x^{9}+22 x^{8}-6 x^{7}+4 x^{6}-x^{5}-37 x^{4}+54 x^{3}-32 x^{2}+9 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,95/8,n = 1,77/8,n = 2,7,n = 3,7/2,n = 4,1,0)+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*(-24*5^(1/2)+40)*(-1/2*5^(1/2)-1/2)^(-n)+1/80*(24*5^(1/2)+40)*(1/2*5^(1/2)-1/2)^(-n)+1/80*(5*n+10)*2^n+n-13
Explicit closed form in latex syntax:
\left(\left\{\begin{array}{cc}\frac{95}{8} & n =0 \\ \frac{77}{8} & n =1 \\ 7 & n =2 \\ \frac{7}{2} & n =3 \\ 1 & n =4 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)+\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(-24 \sqrt{5}+40\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{80}+\frac{\left(24 \sqrt{5}+40\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{80}+\frac{\left(5 n +10\right) 2^{n}}{80}+n -13
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 53
a(6) = 135
a(7) = 333
a(8) = 820
a(9) = 2034
a(10) = 5090
a(11) = 12841
a(12) = 32617
a(n+6) = 4*a(n)-12*a(n+1)-3*a(n+2)+26*a(n+3)-23*a(n+4)+8*a(n+5)+n-15, n >= 13
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) = 135
a \! \left(7\right) = 333
a \! \left(8\right) = 820
a \! \left(9\right) = 2034
a \! \left(10\right) = 5090
a \! \left(11\right) = 12841
a \! \left(12\right) = 32617
a \! \left(n +6\right) = 4 a \! \left(n \right)-12 a \! \left(n +1\right)-3 a \! \left(n +2\right)+26 a \! \left(n +3\right)-23 a \! \left(n +4\right)+8 a \! \left(n +5\right)+n -15, \quad n \geq 13
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16947/
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[24,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[21,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[14,x]*F[4,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[14,x]
F[24,x] = F[25,x]+F[62,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[1,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[17,x]*F[4,x]
F[31,x] = F[25,x]+F[32,x]
F[32,x] = F[33,x]+F[34,x]+F[60,x]
F[33,x] = 0
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[36,x]+F[40,x]
F[36,x] = F[29,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[4,x]
F[40,x] = F[32,x]+F[41,x]
F[41,x] = 2*F[33,x]+F[42,x]+F[46,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = F[37,x]
F[45,x] = F[41,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[33,x]+F[49,x]+F[59,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[53,x]
F[51,x] = F[4,x]+F[52,x]
F[52,x] = F[38,x]
F[53,x] = F[48,x]+F[54,x]
F[54,x] = 2*F[33,x]+F[46,x]+F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[57,x]+F[58,x]
F[57,x] = F[52,x]
F[58,x] = F[54,x]
F[59,x] = F[25,x]*F[4,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[25,x]+F[48,x]
F[62,x] = F[131,x]+F[33,x]+F[63,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[65,x]+F[78,x]
F[65,x] = F[66,x]+F[7,x]
F[66,x] = F[33,x]+F[67,x]+F[72,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[11,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[4,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[29,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[29,x]
F[78,x] = F[62,x]+F[79,x]
F[79,x] = F[107,x]+F[130,x]+F[33,x]+F[80,x]
F[80,x] = F[4,x]*F[81,x]
F[81,x] = F[82,x]+F[86,x]
F[82,x] = F[66,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[69,x]
F[86,x] = F[79,x]+F[87,x]
F[87,x] = 2*F[33,x]+F[106,x]+F[88,x]+F[92,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[83,x]
F[91,x] = F[87,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[97,x]+F[99,x]
F[97,x] = F[69,x]+F[98,x]
F[98,x] = F[84,x]
F[99,x] = F[100,x]+F[94,x]
F[100,x] = 2*F[33,x]+F[101,x]+F[105,x]+F[92,x]
F[101,x] = F[102,x]*F[4,x]
F[102,x] = F[103,x]+F[104,x]
F[103,x] = F[98,x]
F[104,x] = F[100,x]
F[105,x] = 0
F[106,x] = 0
F[107,x] = F[108,x]*F[4,x]
F[108,x] = F[109,x]+F[94,x]
F[109,x] = F[110,x]+F[128,x]+F[33,x]
F[110,x] = F[111,x]*F[4,x]
F[111,x] = F[112,x]+F[114,x]
F[112,x] = F[11,x]+F[113,x]
F[113,x] = F[33,x]+F[67,x]+F[76,x]
F[114,x] = F[109,x]+F[115,x]
F[115,x] = F[107,x]+F[116,x]+F[127,x]+F[33,x]
F[116,x] = F[117,x]*F[4,x]
F[117,x] = F[118,x]+F[120,x]
F[118,x] = F[113,x]+F[119,x]
F[119,x] = F[84,x]
F[120,x] = F[115,x]+F[121,x]
F[121,x] = 2*F[33,x]+F[122,x]+F[126,x]+F[92,x]
F[122,x] = F[123,x]*F[4,x]
F[123,x] = F[124,x]+F[125,x]
F[124,x] = F[119,x]
F[125,x] = F[121,x]
F[126,x] = 0
F[127,x] = 0
F[128,x] = F[129,x]*F[4,x]
F[129,x] = F[25,x]
F[130,x] = 0
F[131,x] = F[132,x]*F[4,x]
F[132,x] = F[133,x]
F[133,x] = F[109,x]+F[25,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_{24}\! \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_{21}\! \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_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{14}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{62}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \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_{34}\! \left(x \right)+F_{60}\! \left(x \right)
F_{33}\! \left(x \right) = 0
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{36}\! \left(x \right) = F_{29}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right)
F_{40}\! \left(x \right) = F_{32}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{42}\! \left(x \right)+F_{46}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{37}\! \left(x \right)
F_{45}\! \left(x \right) = F_{41}\! \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_{48}\! \left(x \right) = F_{33}\! \left(x \right)+F_{49}\! \left(x \right)+F_{59}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{53}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{38}\! \left(x \right)
F_{53}\! \left(x \right) = F_{48}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{46}\! \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_{57}\! \left(x \right)+F_{58}\! \left(x \right)
F_{57}\! \left(x \right) = F_{52}\! \left(x \right)
F_{58}\! \left(x \right) = F_{54}\! \left(x \right)
F_{59}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{25}\! \left(x \right)+F_{48}\! \left(x \right)
F_{62}\! \left(x \right) = F_{131}\! \left(x \right)+F_{33}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{78}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{7}\! \left(x \right)
F_{66}\! \left(x \right) = F_{33}\! \left(x \right)+F_{67}\! \left(x \right)+F_{72}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{11}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{29}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{29}\! \left(x \right)
F_{78}\! \left(x \right) = F_{62}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{107}\! \left(x \right)+F_{130}\! \left(x \right)+F_{33}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{86}\! \left(x \right)
F_{82}\! \left(x \right) = F_{66}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{69}\! \left(x \right)
F_{86}\! \left(x \right) = F_{79}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{106}\! \left(x \right)+F_{88}\! \left(x \right)+F_{92}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{83}\! \left(x \right)
F_{91}\! \left(x \right) = F_{87}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \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_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{97}\! \left(x \right) = F_{69}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{84}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{94}\! \left(x \right)
F_{100}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{101}\! \left(x \right)+F_{105}\! \left(x \right)+F_{92}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{104}\! \left(x \right)
F_{103}\! \left(x \right) = F_{98}\! \left(x \right)
F_{104}\! \left(x \right) = F_{100}\! \left(x \right)
F_{105}\! \left(x \right) = 0
F_{106}\! \left(x \right) = 0
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{94}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{128}\! \left(x \right)+F_{33}\! \left(x \right)
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_{114}\! \left(x \right)
F_{112}\! \left(x \right) = F_{11}\! \left(x \right)+F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{33}\! \left(x \right)+F_{67}\! \left(x \right)+F_{76}\! \left(x \right)
F_{114}\! \left(x \right) = F_{109}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{107}\! \left(x \right)+F_{116}\! \left(x \right)+F_{127}\! \left(x \right)+F_{33}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{4}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{120}\! \left(x \right)
F_{118}\! \left(x \right) = F_{113}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{84}\! \left(x \right)
F_{120}\! \left(x \right) = F_{115}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{122}\! \left(x \right)+F_{126}\! \left(x \right)+F_{92}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{4}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{125}\! \left(x \right)
F_{124}\! \left(x \right) = F_{119}\! \left(x \right)
F_{125}\! \left(x \right) = F_{121}\! \left(x \right)
F_{126}\! \left(x \right) = 0
F_{127}\! \left(x \right) = 0
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{4}\! \left(x \right)
F_{129}\! \left(x \right) = F_{25}\! \left(x \right)
F_{130}\! \left(x \right) = 0
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{4}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{109}\! \left(x \right)+F_{25}\! \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_24(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_21(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_14(x)*F_4(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_14(x))
Eq(F_24(x), F_25(x) + F_62(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_1(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_17(x)*F_4(x))
Eq(F_31(x), F_25(x) + F_32(x))
Eq(F_32(x), F_33(x) + F_34(x) + F_60(x))
Eq(F_33(x), 0)
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_40(x))
Eq(F_36(x), F_29(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_4(x))
Eq(F_40(x), F_32(x) + F_41(x))
Eq(F_41(x), 2*F_33(x) + F_42(x) + F_46(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), F_37(x))
Eq(F_45(x), F_41(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_33(x) + F_49(x) + F_59(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_53(x))
Eq(F_51(x), F_4(x) + F_52(x))
Eq(F_52(x), F_38(x))
Eq(F_53(x), F_48(x) + F_54(x))
Eq(F_54(x), 2*F_33(x) + F_46(x) + F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_58(x))
Eq(F_57(x), F_52(x))
Eq(F_58(x), F_54(x))
Eq(F_59(x), F_25(x)*F_4(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_25(x) + F_48(x))
Eq(F_62(x), F_131(x) + F_33(x) + F_63(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_78(x))
Eq(F_65(x), F_66(x) + F_7(x))
Eq(F_66(x), F_33(x) + F_67(x) + F_72(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_11(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_4(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_29(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_29(x))
Eq(F_78(x), F_62(x) + F_79(x))
Eq(F_79(x), F_107(x) + F_130(x) + F_33(x) + F_80(x))
Eq(F_80(x), F_4(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_86(x))
Eq(F_82(x), F_66(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_69(x))
Eq(F_86(x), F_79(x) + F_87(x))
Eq(F_87(x), F_106(x) + 2*F_33(x) + F_88(x) + F_92(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_83(x))
Eq(F_91(x), F_87(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(x), F_97(x) + F_99(x))
Eq(F_97(x), F_69(x) + F_98(x))
Eq(F_98(x), F_84(x))
Eq(F_99(x), F_100(x) + F_94(x))
Eq(F_100(x), F_101(x) + F_105(x) + 2*F_33(x) + F_92(x))
Eq(F_101(x), F_102(x)*F_4(x))
Eq(F_102(x), F_103(x) + F_104(x))
Eq(F_103(x), F_98(x))
Eq(F_104(x), F_100(x))
Eq(F_105(x), 0)
Eq(F_106(x), 0)
Eq(F_107(x), F_108(x)*F_4(x))
Eq(F_108(x), F_109(x) + F_94(x))
Eq(F_109(x), F_110(x) + F_128(x) + F_33(x))
Eq(F_110(x), F_111(x)*F_4(x))
Eq(F_111(x), F_112(x) + F_114(x))
Eq(F_112(x), F_11(x) + F_113(x))
Eq(F_113(x), F_33(x) + F_67(x) + F_76(x))
Eq(F_114(x), F_109(x) + F_115(x))
Eq(F_115(x), F_107(x) + F_116(x) + F_127(x) + F_33(x))
Eq(F_116(x), F_117(x)*F_4(x))
Eq(F_117(x), F_118(x) + F_120(x))
Eq(F_118(x), F_113(x) + F_119(x))
Eq(F_119(x), F_84(x))
Eq(F_120(x), F_115(x) + F_121(x))
Eq(F_121(x), F_122(x) + F_126(x) + 2*F_33(x) + F_92(x))
Eq(F_122(x), F_123(x)*F_4(x))
Eq(F_123(x), F_124(x) + F_125(x))
Eq(F_124(x), F_119(x))
Eq(F_125(x), F_121(x))
Eq(F_126(x), 0)
Eq(F_127(x), 0)
Eq(F_128(x), F_129(x)*F_4(x))
Eq(F_129(x), F_25(x))
Eq(F_130(x), 0)
Eq(F_131(x), F_132(x)*F_4(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_109(x) + F_25(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, 1, 3], "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, 1, 3], "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, 1, 3], "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, 0, 2], "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, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"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": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 0, 2], "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, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"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": 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