0132_0321_2310
Counting sequence:
1, 1, 2, 6, 21, 74, 246, 763, 2227, 6191, 16567, 43026, 109110, 271384, 664236, 1603813, 3827381, 9040909, 21164253, 49147156, 113305760, 259515246, 590863722, 1337972351, 3014643351, 6761203099, 15099476851, 33587965958, 74440483642, 164416689396, 361985180952, 794568913801, 1739193278505, 3796751043289, 8267811992441, 17961553172968, 38933878472196, 84215718666154, 181797375622838, 391701017303811, 842432065205355, 1808696627579591, 3876877999414767, 8296914743061946, 17729624997739006, 37831996088353424, 80616192548357956, 171558998304950253, 364633240142398557, 774056185954073701, 1641280589199585237, 3476215962376330876, 7354659666472437800, 15544174113868950694, 32819982284462148546, 69229333471938897223, 145894109928666822911, 307181523383686366899, 646212503332137274923, 1358285647614941105966, 2852688090367528536450, 5986544912671052365036, 12553585802911652702512, 26305057049109819969041, 55080824882592113601361, 115255256972537277776049, 241006711323015291096561, 503633006700418177405648, 1051778006850697503624972, 2195162544771436641387106, 4578777026999890062945422, 9545083253500270387154251, 19886770703079614052262995, 41410431688283918877749599, 86183188312371025148736551, 179270476422697471601044578, 372712774660486748489603526, 774505882122484772206427144, 1608664697656578902753612508, 3339657576685413095124229621, 6930091703077135829678071045, 14374127995217940887254683581, 29801230379320223785680106957, 61759184420832946019037777636, 127934574860718132413279050416, 264909497000514461795012810974, 548320394744411208479730960666, 1134494674752595685677863824143, 2346418630399869140737311030887, 4851177528949583952260940497611, 10026076378172294846408004417507, 20713831707342625449749593283926, 42779803422594707504757757670090, 88322070042854741092952913836004, 182286670784772245478896038800456, 376096087455212810556553128923033, 775717987417004987857289217778041, 1599458144837968447338465265770889, 3296921526706081880280144401567593, 6793814935598166948646393737390776, 13995575679982280971561945278821140
Generating function in Maple syntax:
(x^9-23*x^8+133*x^7-315*x^6+419*x^5-350*x^4+188*x^3-63*x^2+12*x-1)/(2*x-1)^4/(-1+x)^5
Generating function in latex syntax:
\frac{x^{9}-23 x^{8}+133 x^{7}-315 x^{6}+419 x^{5}-350 x^{4}+188 x^{3}-63 x^{2}+12 x -1}{\left(2 x -1\right)^{4} \left(-1+x \right)^{5}}
Generating function in sympy syntax:
(x**9 - 23*x**8 + 133*x**7 - 315*x**6 + 419*x**5 - 350*x**4 + 188*x**3 - 63*x**2 + 12*x - 1)/((x - 1)**5*(2*x - 1)**4)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^4*(-1+x)^5*F(x)-x^9+23*x^8-133*x^7+315*x^6-419*x^5+350*x^4-188*x^3+63*x^2-12*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{4} \left(-1+x \right)^{5} F \! \left(x \right)-x^{9}+23 x^{8}-133 x^{7}+315 x^{6}-419 x^{5}+350 x^{4}-188 x^{3}+63 x^{2}-12 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/96*(n^3+6*n^2-n-6)*2^n-1/24*n^4+1/12*n^3+1/24*n^2-1/12*n+1)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(n^{3}+6 n^{2}-n -6\right) 2^{n}}{96}-\frac{n^{4}}{24}+\frac{n^{3}}{12}+\frac{n^{2}}{24}-\frac{n}{12}+1 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 74
a(6) = 246
a(7) = 763
a(8) = 2227
a(9) = 6191
a(n+4) = -16*a(n)+32*a(n+1)-24*a(n+2)+8*a(n+3)-1/24*(n+1)*(n^3-19*n^2+90*n-96), 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) = 21
a \! \left(5\right) = 74
a \! \left(6\right) = 246
a \! \left(7\right) = 763
a \! \left(8\right) = 2227
a \! \left(9\right) = 6191
a \! \left(n +4\right) = -16 a \! \left(n \right)+32 a \! \left(n +1\right)-24 a \! \left(n +2\right)+8 a \! \left(n +3\right)-\frac{\left(n +1\right) \left(n^{3}-19 n^{2}+90 n -96\right)}{24}, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14703/
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[12,x]*F[4,x]
F[4,x] = F[20,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[10,x]+F[14,x]
F[14,x] = F[15,x]+F[16,x]+F[19,x]
F[15,x] = 0
F[16,x] = F[12,x]*F[17,x]
F[17,x] = F[10,x]+F[18,x]
F[18,x] = F[16,x]
F[19,x] = F[12,x]*F[13,x]
F[20,x] = F[21,x]+F[52,x]
F[21,x] = F[22,x]
F[22,x] = F[12,x]*F[23,x]
F[23,x] = F[24,x]+F[32,x]
F[24,x] = F[1,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[28,x]+F[9,x]
F[28,x] = F[12,x]+F[29,x]
F[29,x] = F[15,x]+F[30,x]+F[31,x]
F[30,x] = F[10,x]*F[12,x]
F[31,x] = F[12,x]*F[28,x]
F[32,x] = F[33,x]+F[36,x]
F[33,x] = F[34,x]
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[1,x]+F[33,x]
F[36,x] = F[15,x]+F[37,x]+F[39,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[25,x]+F[36,x]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[41,x]+F[46,x]
F[41,x] = F[33,x]+F[42,x]
F[42,x] = F[15,x]+F[43,x]+F[45,x]
F[43,x] = F[12,x]*F[44,x]
F[44,x] = F[10,x]+F[42,x]
F[45,x] = F[12,x]*F[41,x]
F[46,x] = F[47,x]+F[49,x]
F[47,x] = F[48,x]
F[48,x] = F[12,x]*F[33,x]
F[49,x] = 2*F[15,x]+F[50,x]+F[51,x]
F[50,x] = F[12,x]*F[42,x]
F[51,x] = F[12,x]*F[46,x]
F[52,x] = F[108,x]+F[15,x]+F[53,x]
F[53,x] = F[12,x]*F[54,x]
F[54,x] = F[55,x]+F[71,x]
F[55,x] = F[56,x]+F[6,x]
F[56,x] = F[15,x]+F[57,x]+F[63,x]
F[57,x] = F[12,x]*F[58,x]
F[58,x] = F[17,x]+F[59,x]
F[59,x] = F[29,x]+F[60,x]
F[60,x] = 2*F[15,x]+F[61,x]+F[62,x]
F[61,x] = F[12,x]*F[18,x]
F[62,x] = F[12,x]*F[59,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[13,x]+F[65,x]
F[65,x] = F[18,x]+F[66,x]
F[66,x] = 2*F[15,x]+F[67,x]+F[70,x]
F[67,x] = F[12,x]*F[68,x]
F[68,x] = F[18,x]+F[69,x]
F[69,x] = F[67,x]
F[70,x] = F[12,x]*F[65,x]
F[71,x] = F[72,x]+F[87,x]
F[72,x] = F[15,x]+F[73,x]+F[75,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[6,x]+F[72,x]
F[75,x] = F[12,x]*F[76,x]
F[76,x] = F[41,x]+F[77,x]
F[77,x] = F[42,x]+F[78,x]
F[78,x] = F[15,x]+F[79,x]+F[81,x]+F[86,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[14,x]+F[78,x]
F[81,x] = F[12,x]*F[82,x]
F[82,x] = F[42,x]+F[83,x]
F[83,x] = 2*F[15,x]+F[81,x]+F[84,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[18,x]+F[83,x]
F[86,x] = F[12,x]*F[77,x]
F[87,x] = F[15,x]+F[88,x]+F[90,x]+F[96,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[56,x]+F[87,x]
F[90,x] = F[12,x]*F[91,x]
F[91,x] = F[82,x]+F[92,x]
F[92,x] = F[49,x]+F[93,x]
F[93,x] = 3*F[15,x]+F[94,x]+F[95,x]
F[94,x] = F[12,x]*F[83,x]
F[95,x] = F[12,x]*F[92,x]
F[96,x] = F[12,x]*F[97,x]
F[97,x] = F[77,x]+F[98,x]
F[98,x] = F[83,x]+F[99,x]
F[99,x] = 2*F[15,x]+F[100,x]+F[102,x]+F[107,x]
F[100,x] = F[101,x]*F[12,x]
F[101,x] = F[66,x]+F[99,x]
F[102,x] = F[103,x]*F[12,x]
F[103,x] = F[104,x]+F[83,x]
F[104,x] = 3*F[15,x]+F[102,x]+F[105,x]
F[105,x] = F[106,x]*F[12,x]
F[106,x] = F[104,x]+F[69,x]
F[107,x] = F[12,x]*F[98,x]
F[108,x] = F[109,x]*F[12,x]
F[109,x] = F[110,x]+F[121,x]
F[110,x] = F[111,x]+F[21,x]
F[111,x] = F[112,x]+F[120,x]+F[15,x]
F[112,x] = F[113,x]*F[12,x]
F[113,x] = F[114,x]+F[116,x]
F[114,x] = F[10,x]+F[115,x]
F[115,x] = F[15,x]+F[19,x]+F[57,x]
F[116,x] = F[117,x]+F[42,x]
F[117,x] = F[118,x]+F[15,x]+F[86,x]+F[90,x]
F[118,x] = F[119,x]*F[12,x]
F[119,x] = F[115,x]+F[117,x]
F[120,x] = F[110,x]*F[12,x]
F[121,x] = F[122,x]+F[131,x]
F[122,x] = F[123,x]+F[15,x]+F[45,x]
F[123,x] = F[12,x]*F[124,x]
F[124,x] = F[125,x]+F[127,x]
F[125,x] = F[10,x]+F[126,x]
F[126,x] = F[15,x]+F[31,x]+F[57,x]
F[127,x] = F[128,x]+F[42,x]
F[128,x] = F[129,x]+F[15,x]+F[51,x]+F[90,x]
F[129,x] = F[12,x]*F[130,x]
F[130,x] = F[126,x]+F[128,x]
F[131,x] = F[132,x]+F[15,x]+F[152,x]+F[81,x]
F[132,x] = F[12,x]*F[133,x]
F[133,x] = F[134,x]+F[142,x]
F[134,x] = F[135,x]+F[14,x]
F[135,x] = F[136,x]+F[15,x]+F[62,x]+F[70,x]
F[136,x] = F[12,x]*F[137,x]
F[137,x] = F[138,x]+F[68,x]
F[138,x] = F[139,x]+F[60,x]
F[139,x] = 3*F[15,x]+F[140,x]+F[141,x]
F[140,x] = F[12,x]*F[69,x]
F[141,x] = F[12,x]*F[138,x]
F[142,x] = F[143,x]+F[78,x]
F[143,x] = F[107,x]+F[144,x]+F[146,x]+F[15,x]+F[95,x]
F[144,x] = F[12,x]*F[145,x]
F[145,x] = F[135,x]+F[143,x]
F[146,x] = F[12,x]*F[147,x]
F[147,x] = F[103,x]+F[148,x]
F[148,x] = F[149,x]+F[93,x]
F[149,x] = 4*F[15,x]+F[150,x]+F[151,x]
F[150,x] = F[104,x]*F[12,x]
F[151,x] = F[12,x]*F[148,x]
F[152,x] = F[12,x]*F[121,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{20}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{10}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{16}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{52}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{32}\! \left(x \right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{9}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{15}\! \left(x \right)+F_{30}\! \left(x \right)+F_{31}\! \left(x \right)
F_{30}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{36}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{1}\! \left(x \right)+F_{33}\! \left(x \right)
F_{36}\! \left(x \right) = F_{15}\! \left(x \right)+F_{37}\! \left(x \right)+F_{39}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{25}\! \left(x \right)+F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{46}\! \left(x \right)
F_{41}\! \left(x \right) = F_{33}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{15}\! \left(x \right)+F_{43}\! \left(x \right)+F_{45}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{10}\! \left(x \right)+F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{49}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{49}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{50}\! \left(x \right)+F_{51}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{52}\! \left(x \right) = F_{108}\! \left(x \right)+F_{15}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{71}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{6}\! \left(x \right)
F_{56}\! \left(x \right) = F_{15}\! \left(x \right)+F_{57}\! \left(x \right)+F_{63}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{17}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{29}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{13}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{18}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{67}\! \left(x \right)+F_{70}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{18}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{87}\! \left(x \right)
F_{72}\! \left(x \right) = F_{15}\! \left(x \right)+F_{73}\! \left(x \right)+F_{75}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{6}\! \left(x \right)+F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{41}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{42}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{15}\! \left(x \right)+F_{79}\! \left(x \right)+F_{81}\! \left(x \right)+F_{86}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{14}\! \left(x \right)+F_{78}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{42}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{81}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{18}\! \left(x \right)+F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{87}\! \left(x \right) = F_{15}\! \left(x \right)+F_{88}\! \left(x \right)+F_{90}\! \left(x \right)+F_{96}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{56}\! \left(x \right)+F_{87}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{82}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{49}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \left(x \right)
F_{95}\! \left(x \right) = F_{12}\! \left(x \right) F_{92}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{77}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{83}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{100}\! \left(x \right)+F_{102}\! \left(x \right)+F_{107}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{12}\! \left(x \right)
F_{101}\! \left(x \right) = F_{66}\! \left(x \right)+F_{99}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{12}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{83}\! \left(x \right)
F_{104}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{102}\! \left(x \right)+F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{12}\! \left(x \right)
F_{106}\! \left(x \right) = F_{104}\! \left(x \right)+F_{69}\! \left(x \right)
F_{107}\! \left(x \right) = F_{12}\! \left(x \right) F_{98}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{12}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{121}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{21}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{120}\! \left(x \right)+F_{15}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{12}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{116}\! \left(x \right)
F_{114}\! \left(x \right) = F_{10}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{15}\! \left(x \right)+F_{19}\! \left(x \right)+F_{57}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{42}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{15}\! \left(x \right)+F_{86}\! \left(x \right)+F_{90}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{12}\! \left(x \right)
F_{119}\! \left(x \right) = F_{115}\! \left(x \right)+F_{117}\! \left(x \right)
F_{120}\! \left(x \right) = F_{110}\! \left(x \right) F_{12}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{131}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{15}\! \left(x \right)+F_{45}\! \left(x \right)
F_{123}\! \left(x \right) = F_{12}\! \left(x \right) F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{127}\! \left(x \right)
F_{125}\! \left(x \right) = F_{10}\! \left(x \right)+F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{15}\! \left(x \right)+F_{31}\! \left(x \right)+F_{57}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{42}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{15}\! \left(x \right)+F_{51}\! \left(x \right)+F_{90}\! \left(x \right)
F_{129}\! \left(x \right) = F_{12}\! \left(x \right) F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{126}\! \left(x \right)+F_{128}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{15}\! \left(x \right)+F_{152}\! \left(x \right)+F_{81}\! \left(x \right)
F_{132}\! \left(x \right) = F_{12}\! \left(x \right) F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{142}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{14}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{15}\! \left(x \right)+F_{62}\! \left(x \right)+F_{70}\! \left(x \right)
F_{136}\! \left(x \right) = F_{12}\! \left(x \right) F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{68}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{60}\! \left(x \right)
F_{139}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{140}\! \left(x \right)+F_{141}\! \left(x \right)
F_{140}\! \left(x \right) = F_{12}\! \left(x \right) F_{69}\! \left(x \right)
F_{141}\! \left(x \right) = F_{12}\! \left(x \right) F_{138}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{78}\! \left(x \right)
F_{143}\! \left(x \right) = F_{107}\! \left(x \right)+F_{144}\! \left(x \right)+F_{146}\! \left(x \right)+F_{15}\! \left(x \right)+F_{95}\! \left(x \right)
F_{144}\! \left(x \right) = F_{12}\! \left(x \right) F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{135}\! \left(x \right)+F_{143}\! \left(x \right)
F_{146}\! \left(x \right) = F_{12}\! \left(x \right) F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{103}\! \left(x \right)+F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{93}\! \left(x \right)
F_{149}\! \left(x \right) = 4 F_{15}\! \left(x \right)+F_{150}\! \left(x \right)+F_{151}\! \left(x \right)
F_{150}\! \left(x \right) = F_{104}\! \left(x \right) F_{12}\! \left(x \right)
F_{151}\! \left(x \right) = F_{12}\! \left(x \right) F_{148}\! \left(x \right)
F_{152}\! \left(x \right) = F_{12}\! \left(x \right) F_{121}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_20(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_10(x) + F_14(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_19(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_12(x)*F_17(x))
Eq(F_17(x), F_10(x) + F_18(x))
Eq(F_18(x), F_16(x))
Eq(F_19(x), F_12(x)*F_13(x))
Eq(F_20(x), F_21(x) + F_52(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_12(x)*F_23(x))
Eq(F_23(x), F_24(x) + F_32(x))
Eq(F_24(x), F_1(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_9(x))
Eq(F_28(x), F_12(x) + F_29(x))
Eq(F_29(x), F_15(x) + F_30(x) + F_31(x))
Eq(F_30(x), F_10(x)*F_12(x))
Eq(F_31(x), F_12(x)*F_28(x))
Eq(F_32(x), F_33(x) + F_36(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_1(x) + F_33(x))
Eq(F_36(x), F_15(x) + F_37(x) + F_39(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_25(x) + F_36(x))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_46(x))
Eq(F_41(x), F_33(x) + F_42(x))
Eq(F_42(x), F_15(x) + F_43(x) + F_45(x))
Eq(F_43(x), F_12(x)*F_44(x))
Eq(F_44(x), F_10(x) + F_42(x))
Eq(F_45(x), F_12(x)*F_41(x))
Eq(F_46(x), F_47(x) + F_49(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_12(x)*F_33(x))
Eq(F_49(x), 2*F_15(x) + F_50(x) + F_51(x))
Eq(F_50(x), F_12(x)*F_42(x))
Eq(F_51(x), F_12(x)*F_46(x))
Eq(F_52(x), F_108(x) + F_15(x) + F_53(x))
Eq(F_53(x), F_12(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_71(x))
Eq(F_55(x), F_56(x) + F_6(x))
Eq(F_56(x), F_15(x) + F_57(x) + F_63(x))
Eq(F_57(x), F_12(x)*F_58(x))
Eq(F_58(x), F_17(x) + F_59(x))
Eq(F_59(x), F_29(x) + F_60(x))
Eq(F_60(x), 2*F_15(x) + F_61(x) + F_62(x))
Eq(F_61(x), F_12(x)*F_18(x))
Eq(F_62(x), F_12(x)*F_59(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_13(x) + F_65(x))
Eq(F_65(x), F_18(x) + F_66(x))
Eq(F_66(x), 2*F_15(x) + F_67(x) + F_70(x))
Eq(F_67(x), F_12(x)*F_68(x))
Eq(F_68(x), F_18(x) + F_69(x))
Eq(F_69(x), F_67(x))
Eq(F_70(x), F_12(x)*F_65(x))
Eq(F_71(x), F_72(x) + F_87(x))
Eq(F_72(x), F_15(x) + F_73(x) + F_75(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_6(x) + F_72(x))
Eq(F_75(x), F_12(x)*F_76(x))
Eq(F_76(x), F_41(x) + F_77(x))
Eq(F_77(x), F_42(x) + F_78(x))
Eq(F_78(x), F_15(x) + F_79(x) + F_81(x) + F_86(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_14(x) + F_78(x))
Eq(F_81(x), F_12(x)*F_82(x))
Eq(F_82(x), F_42(x) + F_83(x))
Eq(F_83(x), 2*F_15(x) + F_81(x) + F_84(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_18(x) + F_83(x))
Eq(F_86(x), F_12(x)*F_77(x))
Eq(F_87(x), F_15(x) + F_88(x) + F_90(x) + F_96(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_56(x) + F_87(x))
Eq(F_90(x), F_12(x)*F_91(x))
Eq(F_91(x), F_82(x) + F_92(x))
Eq(F_92(x), F_49(x) + F_93(x))
Eq(F_93(x), 3*F_15(x) + F_94(x) + F_95(x))
Eq(F_94(x), F_12(x)*F_83(x))
Eq(F_95(x), F_12(x)*F_92(x))
Eq(F_96(x), F_12(x)*F_97(x))
Eq(F_97(x), F_77(x) + F_98(x))
Eq(F_98(x), F_83(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_102(x) + F_107(x) + 2*F_15(x))
Eq(F_100(x), F_101(x)*F_12(x))
Eq(F_101(x), F_66(x) + F_99(x))
Eq(F_102(x), F_103(x)*F_12(x))
Eq(F_103(x), F_104(x) + F_83(x))
Eq(F_104(x), F_102(x) + F_105(x) + 3*F_15(x))
Eq(F_105(x), F_106(x)*F_12(x))
Eq(F_106(x), F_104(x) + F_69(x))
Eq(F_107(x), F_12(x)*F_98(x))
Eq(F_108(x), F_109(x)*F_12(x))
Eq(F_109(x), F_110(x) + F_121(x))
Eq(F_110(x), F_111(x) + F_21(x))
Eq(F_111(x), F_112(x) + F_120(x) + F_15(x))
Eq(F_112(x), F_113(x)*F_12(x))
Eq(F_113(x), F_114(x) + F_116(x))
Eq(F_114(x), F_10(x) + F_115(x))
Eq(F_115(x), F_15(x) + F_19(x) + F_57(x))
Eq(F_116(x), F_117(x) + F_42(x))
Eq(F_117(x), F_118(x) + F_15(x) + F_86(x) + F_90(x))
Eq(F_118(x), F_119(x)*F_12(x))
Eq(F_119(x), F_115(x) + F_117(x))
Eq(F_120(x), F_110(x)*F_12(x))
Eq(F_121(x), F_122(x) + F_131(x))
Eq(F_122(x), F_123(x) + F_15(x) + F_45(x))
Eq(F_123(x), F_12(x)*F_124(x))
Eq(F_124(x), F_125(x) + F_127(x))
Eq(F_125(x), F_10(x) + F_126(x))
Eq(F_126(x), F_15(x) + F_31(x) + F_57(x))
Eq(F_127(x), F_128(x) + F_42(x))
Eq(F_128(x), F_129(x) + F_15(x) + F_51(x) + F_90(x))
Eq(F_129(x), F_12(x)*F_130(x))
Eq(F_130(x), F_126(x) + F_128(x))
Eq(F_131(x), F_132(x) + F_15(x) + F_152(x) + F_81(x))
Eq(F_132(x), F_12(x)*F_133(x))
Eq(F_133(x), F_134(x) + F_142(x))
Eq(F_134(x), F_135(x) + F_14(x))
Eq(F_135(x), F_136(x) + F_15(x) + F_62(x) + F_70(x))
Eq(F_136(x), F_12(x)*F_137(x))
Eq(F_137(x), F_138(x) + F_68(x))
Eq(F_138(x), F_139(x) + F_60(x))
Eq(F_139(x), F_140(x) + F_141(x) + 3*F_15(x))
Eq(F_140(x), F_12(x)*F_69(x))
Eq(F_141(x), F_12(x)*F_138(x))
Eq(F_142(x), F_143(x) + F_78(x))
Eq(F_143(x), F_107(x) + F_144(x) + F_146(x) + F_15(x) + F_95(x))
Eq(F_144(x), F_12(x)*F_145(x))
Eq(F_145(x), F_135(x) + F_143(x))
Eq(F_146(x), F_12(x)*F_147(x))
Eq(F_147(x), F_103(x) + F_148(x))
Eq(F_148(x), F_149(x) + F_93(x))
Eq(F_149(x), 4*F_15(x) + F_150(x) + F_151(x))
Eq(F_150(x), F_104(x)*F_12(x))
Eq(F_151(x), F_12(x)*F_148(x))
Eq(F_152(x), F_12(x)*F_121(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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "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": 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