0132_1230_3120
Counting sequence:
1, 1, 2, 6, 21, 74, 248, 784, 2355, 6785, 18897, 51177, 135358, 350788, 893038, 2237998, 5530485, 13496371, 32566359, 77785039, 184083080, 432004206, 1006097772, 2326777196, 5346673751, 12213795349, 27749494413, 62729986469, 141146690370, 316216935240, 705582559642, 1568468327962, 3474360060073, 7670811537703, 16883516381043, 37052682795883, 81093277441260, 177021371988946, 385481904658424, 837484262879544, 1815499855775595, 3927455534291561, 8479433673271817, 18272783741859361, 39306441181200006, 84407308640928524, 180962021745689478, 387362344511782854, 827941051808118685, 1767099903789247195, 3766416663365015887, 8017251761649320647, 17044154264760035088, 36190926605548963318, 76757100249088679748, 162611471745466102468, 344124551127006543935, 727493469406919985021, 1536412020076698961989, 3241654982984263533149, 6833149585022667683210, 14390766220502663356816, 30280906857746531763762, 63663172562885482488626, 133737741612889641646161, 280722551313711955723599, 588801624088735177214443, 1234068731787095292691939, 2584628652399666404653300, 5409470806127178591314650, 11314052223192721548919632, 23648135606685286464969232, 49396838854532026992584403, 103117594519941572885047633, 215132127493609557353849153, 448563425108338989911985753, 934749943985700443242770510, 1946823916761908457215952596, 4052508242007551779422065054, 8431275339583601607369461854, 17532371141097433691851145925, 36439442054824152583991715971, 75699308046809235032574689607, 157183326140474470666120268991, 326227423497188068165284760216, 676766345226826329033912744574, 1403350105628332297099119713308, 2908752893245253130610238205724, 6026504882185483352943682450215, 12480911476075203931532967749605, 25837665529944814407557068442877, 53467558751765038108099346653717, 110601586414883551245381177272018, 228701994617738293505963802450648, 472737114562065307096828160589258, 976818870918836442754102149713738, 2017698662990612743973684183092985, 4166292153975104456694102168599671, 8599979356435851052766415173195619, 17746078437082526184565128799821659, 36607293261553322920759388704543740
Generating function in Maple syntax:
(x^9-26*x^8+138*x^7-317*x^6+419*x^5-350*x^4+188*x^3-63*x^2+12*x-1)/(2*x-1)^4/(x-1)^5
Generating function in latex syntax:
\frac{x^{9}-26 x^{8}+138 x^{7}-317 x^{6}+419 x^{5}-350 x^{4}+188 x^{3}-63 x^{2}+12 x -1}{\left(2 x -1\right)^{4} \left(x -1\right)^{5}}
Generating function in sympy syntax:
(x**9 - 26*x**8 + 138*x**7 - 317*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*(x-1)^5*F(x)-x^9+26*x^8-138*x^7+317*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(x -1\right)^{5} F \! \left(x \right)-x^{9}+26 x^{8}-138 x^{7}+317 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*(3*n^3-24*n^2+123*n-6)*2^n-1/24*n^4-1/12*n^3-11/24*n^2-17/12*n+1)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(3 n^{3}-24 n^{2}+123 n -6\right) 2^{n}}{96}-\frac{n^{4}}{24}-\frac{n^{3}}{12}-\frac{11 n^{2}}{24}-\frac{17 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) = 248
a(7) = 784
a(8) = 2355
a(9) = 6785
a(n+4) = -16*a(n)+32*a(n+1)-24*a(n+2)+8*a(n+3)-1/24*(n-2)*(n-3)*(n^2-9*n-16), 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) = 248
a \! \left(7\right) = 784
a \! \left(8\right) = 2355
a \! \left(9\right) = 6785
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 -2\right) \left(n -3\right) \left(n^{2}-9 n -16\right)}{24}, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14729/
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[38,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[14,x]+F[24,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[12,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]*F[21,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[12,x]
F[23,x] = F[19,x]
F[24,x] = F[25,x]+F[26,x]+F[37,x]
F[25,x] = 0
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[10,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[10,x]*F[12,x]
F[31,x] = F[24,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[29,x]
F[36,x] = F[32,x]
F[37,x] = F[12,x]*F[13,x]
F[38,x] = F[39,x]+F[51,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[42,x]+F[45,x]
F[42,x] = F[1,x]+F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[12,x]*F[42,x]
F[45,x] = F[39,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[43,x]
F[50,x] = F[46,x]
F[51,x] = F[146,x]+F[25,x]+F[52,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[54,x]+F[91,x]
F[54,x] = F[55,x]+F[6,x]
F[55,x] = F[25,x]+F[56,x]+F[61,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[10,x]+F[58,x]
F[58,x] = F[25,x]+F[56,x]+F[59,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = F[43,x]+F[58,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[60,x]+F[63,x]
F[63,x] = F[64,x]+F[77,x]
F[64,x] = F[25,x]+F[65,x]+F[68,x]
F[65,x] = F[12,x]*F[66,x]
F[66,x] = F[12,x]+F[67,x]
F[67,x] = F[65,x]
F[68,x] = F[12,x]*F[69,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[43,x]+F[67,x]
F[71,x] = F[64,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = F[67,x]
F[76,x] = F[72,x]
F[77,x] = F[25,x]+F[78,x]+F[81,x]+F[90,x]
F[78,x] = F[12,x]*F[79,x]
F[79,x] = F[29,x]+F[80,x]
F[80,x] = F[78,x]
F[81,x] = F[12,x]*F[82,x]
F[82,x] = F[83,x]+F[84,x]
F[83,x] = F[58,x]+F[80,x]
F[84,x] = F[77,x]+F[85,x]
F[85,x] = F[86,x]
F[86,x] = F[12,x]*F[87,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[80,x]
F[89,x] = F[85,x]
F[90,x] = F[12,x]*F[63,x]
F[91,x] = F[51,x]+F[92,x]
F[92,x] = 2*F[25,x]+F[93,x]+F[97,x]
F[93,x] = F[12,x]*F[94,x]
F[94,x] = F[95,x]+F[96,x]
F[95,x] = F[55,x]
F[96,x] = F[92,x]
F[97,x] = F[12,x]*F[98,x]
F[98,x] = F[106,x]+F[99,x]
F[99,x] = F[100,x]+F[46,x]
F[100,x] = 2*F[25,x]+F[101,x]+F[105,x]
F[101,x] = F[102,x]*F[12,x]
F[102,x] = F[103,x]+F[104,x]
F[103,x] = F[58,x]
F[104,x] = F[100,x]
F[105,x] = F[12,x]*F[99,x]
F[106,x] = F[107,x]+F[124,x]
F[107,x] = 2*F[25,x]+F[108,x]+F[120,x]
F[108,x] = F[109,x]*F[12,x]
F[109,x] = F[110,x]+F[114,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]
F[112,x] = F[113,x]*F[12,x]
F[113,x] = F[111,x]+F[43,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[12,x]
F[117,x] = F[118,x]+F[119,x]
F[118,x] = F[111,x]
F[119,x] = F[115,x]
F[120,x] = F[12,x]*F[121,x]
F[121,x] = F[122,x]+F[123,x]
F[122,x] = F[46,x]
F[123,x] = F[107,x]
F[124,x] = 2*F[25,x]+F[125,x]+F[141,x]+F[145,x]
F[125,x] = F[12,x]*F[126,x]
F[126,x] = F[127,x]+F[133,x]
F[127,x] = F[128,x]
F[128,x] = 2*F[25,x]+F[129,x]+F[131,x]
F[129,x] = F[12,x]*F[130,x]
F[130,x] = F[128,x]+F[58,x]
F[131,x] = F[12,x]*F[132,x]
F[132,x] = F[111,x]+F[128,x]
F[133,x] = F[134,x]
F[134,x] = 3*F[25,x]+F[135,x]+F[139,x]
F[135,x] = F[12,x]*F[136,x]
F[136,x] = F[137,x]+F[138,x]
F[137,x] = F[128,x]
F[138,x] = F[134,x]
F[139,x] = F[12,x]*F[140,x]
F[140,x] = F[115,x]+F[134,x]
F[141,x] = F[12,x]*F[142,x]
F[142,x] = F[143,x]+F[144,x]
F[143,x] = F[100,x]
F[144,x] = F[124,x]
F[145,x] = F[106,x]*F[12,x]
F[146,x] = F[12,x]*F[147,x]
F[147,x] = F[148,x]+F[154,x]
F[148,x] = F[149,x]+F[39,x]
F[149,x] = F[150,x]+F[153,x]+F[25,x]
F[150,x] = F[12,x]*F[151,x]
F[151,x] = F[152,x]+F[57,x]
F[152,x] = F[100,x]+F[149,x]
F[153,x] = F[12,x]*F[148,x]
F[154,x] = F[155,x]+F[174,x]
F[155,x] = F[156,x]+F[160,x]+F[25,x]
F[156,x] = F[12,x]*F[157,x]
F[157,x] = F[158,x]+F[159,x]
F[158,x] = F[111,x]+F[43,x]
F[159,x] = F[115,x]+F[46,x]
F[160,x] = F[12,x]*F[161,x]
F[161,x] = F[162,x]+F[168,x]
F[162,x] = F[163,x]+F[39,x]
F[163,x] = F[164,x]
F[164,x] = F[12,x]*F[165,x]
F[165,x] = F[166,x]+F[167,x]
F[166,x] = F[12,x]
F[167,x] = F[163,x]
F[168,x] = F[155,x]+F[169,x]
F[169,x] = F[170,x]
F[170,x] = F[12,x]*F[171,x]
F[171,x] = F[172,x]+F[173,x]
F[172,x] = F[163,x]
F[173,x] = F[169,x]
F[174,x] = F[175,x]+F[179,x]+F[193,x]+F[25,x]
F[175,x] = F[12,x]*F[176,x]
F[176,x] = F[177,x]+F[178,x]
F[177,x] = F[128,x]+F[58,x]
F[178,x] = F[100,x]+F[134,x]
F[179,x] = F[12,x]*F[180,x]
F[180,x] = F[181,x]+F[187,x]
F[181,x] = F[149,x]+F[182,x]
F[182,x] = F[183,x]
F[183,x] = F[12,x]*F[184,x]
F[184,x] = F[185,x]+F[186,x]
F[185,x] = F[29,x]
F[186,x] = F[182,x]
F[187,x] = F[174,x]+F[188,x]
F[188,x] = F[189,x]
F[189,x] = F[12,x]*F[190,x]
F[190,x] = F[191,x]+F[192,x]
F[191,x] = F[182,x]
F[192,x] = F[188,x]
F[193,x] = F[12,x]*F[154,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_{38}\! \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_{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_{12}\! \left(x \right) F_{16}\! \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_{12}\! \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_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{37}\! \left(x \right)
F_{25}\! \left(x \right) = 0
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_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{10}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{31}\! \left(x \right) = F_{24}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right)
F_{36}\! \left(x \right) = F_{32}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{51}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{45}\! \left(x \right)
F_{42}\! \left(x \right) = F_{1}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{39}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{43}\! \left(x \right)
F_{50}\! \left(x \right) = F_{46}\! \left(x \right)
F_{51}\! \left(x \right) = F_{146}\! \left(x \right)+F_{25}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{91}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{6}\! \left(x \right)
F_{55}\! \left(x \right) = F_{25}\! \left(x \right)+F_{56}\! \left(x \right)+F_{61}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{10}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{25}\! \left(x \right)+F_{56}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{43}\! \left(x \right)+F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{60}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{77}\! \left(x \right)
F_{64}\! \left(x \right) = F_{25}\! \left(x \right)+F_{65}\! \left(x \right)+F_{68}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{65}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \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_{43}\! \left(x \right)+F_{67}\! \left(x \right)
F_{71}\! \left(x \right) = F_{64}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{67}\! \left(x \right)
F_{76}\! \left(x \right) = F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = F_{25}\! \left(x \right)+F_{78}\! \left(x \right)+F_{81}\! \left(x \right)+F_{90}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{29}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \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_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = F_{58}\! \left(x \right)+F_{80}\! \left(x \right)
F_{84}\! \left(x \right) = F_{77}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{12}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{80}\! \left(x \right)
F_{89}\! \left(x \right) = F_{85}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{91}\! \left(x \right) = F_{51}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{93}\! \left(x \right)+F_{97}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{96}\! \left(x \right)
F_{95}\! \left(x \right) = F_{55}\! \left(x \right)
F_{96}\! \left(x \right) = F_{92}\! \left(x \right)
F_{97}\! \left(x \right) = F_{12}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{106}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{46}\! \left(x \right)
F_{100}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{101}\! \left(x \right)+F_{105}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{12}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{104}\! \left(x \right)
F_{103}\! \left(x \right) = F_{58}\! \left(x \right)
F_{104}\! \left(x \right) = F_{100}\! \left(x \right)
F_{105}\! \left(x \right) = F_{12}\! \left(x \right) F_{99}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{124}\! \left(x \right)
F_{107}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{108}\! \left(x \right)+F_{120}\! \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_{114}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{12}\! \left(x \right)
F_{113}\! \left(x \right) = F_{111}\! \left(x \right)+F_{43}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{12}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{119}\! \left(x \right)
F_{118}\! \left(x \right) = F_{111}\! \left(x \right)
F_{119}\! \left(x \right) = F_{115}\! \left(x \right)
F_{120}\! \left(x \right) = F_{12}\! \left(x \right) F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{123}\! \left(x \right)
F_{122}\! \left(x \right) = F_{46}\! \left(x \right)
F_{123}\! \left(x \right) = F_{107}\! \left(x \right)
F_{124}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{125}\! \left(x \right)+F_{141}\! \left(x \right)+F_{145}\! \left(x \right)
F_{125}\! \left(x \right) = F_{12}\! \left(x \right) F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{133}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{129}\! \left(x \right)+F_{131}\! \left(x \right)
F_{129}\! \left(x \right) = F_{12}\! \left(x \right) F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{128}\! \left(x \right)+F_{58}\! \left(x \right)
F_{131}\! \left(x \right) = F_{12}\! \left(x \right) F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{111}\! \left(x \right)+F_{128}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = 3 F_{25}\! \left(x \right)+F_{135}\! \left(x \right)+F_{139}\! \left(x \right)
F_{135}\! \left(x \right) = F_{12}\! \left(x \right) F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{138}\! \left(x \right)
F_{137}\! \left(x \right) = F_{128}\! \left(x \right)
F_{138}\! \left(x \right) = F_{134}\! \left(x \right)
F_{139}\! \left(x \right) = F_{12}\! \left(x \right) F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{115}\! \left(x \right)+F_{134}\! \left(x \right)
F_{141}\! \left(x \right) = F_{12}\! \left(x \right) F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{144}\! \left(x \right)
F_{143}\! \left(x \right) = F_{100}\! \left(x \right)
F_{144}\! \left(x \right) = F_{124}\! \left(x \right)
F_{145}\! \left(x \right) = F_{106}\! \left(x \right) F_{12}\! \left(x \right)
F_{146}\! \left(x \right) = F_{12}\! \left(x \right) F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{154}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{39}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{153}\! \left(x \right)+F_{25}\! \left(x \right)
F_{150}\! \left(x \right) = F_{12}\! \left(x \right) F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{57}\! \left(x \right)
F_{152}\! \left(x \right) = F_{100}\! \left(x \right)+F_{149}\! \left(x \right)
F_{153}\! \left(x \right) = F_{12}\! \left(x \right) F_{148}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{174}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{160}\! \left(x \right)+F_{25}\! \left(x \right)
F_{156}\! \left(x \right) = F_{12}\! \left(x \right) F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{159}\! \left(x \right)
F_{158}\! \left(x \right) = F_{111}\! \left(x \right)+F_{43}\! \left(x \right)
F_{159}\! \left(x \right) = F_{115}\! \left(x \right)+F_{46}\! \left(x \right)
F_{160}\! \left(x \right) = F_{12}\! \left(x \right) F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{168}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{39}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{12}\! \left(x \right) F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)+F_{167}\! \left(x \right)
F_{166}\! \left(x \right) = F_{12}\! \left(x \right)
F_{167}\! \left(x \right) = F_{163}\! \left(x \right)
F_{168}\! \left(x \right) = F_{155}\! \left(x \right)+F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{12}\! \left(x \right) F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{173}\! \left(x \right)
F_{172}\! \left(x \right) = F_{163}\! \left(x \right)
F_{173}\! \left(x \right) = F_{169}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)+F_{179}\! \left(x \right)+F_{193}\! \left(x \right)+F_{25}\! \left(x \right)
F_{175}\! \left(x \right) = F_{12}\! \left(x \right) F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)+F_{178}\! \left(x \right)
F_{177}\! \left(x \right) = F_{128}\! \left(x \right)+F_{58}\! \left(x \right)
F_{178}\! \left(x \right) = F_{100}\! \left(x \right)+F_{134}\! \left(x \right)
F_{179}\! \left(x \right) = F_{12}\! \left(x \right) F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{187}\! \left(x \right)
F_{181}\! \left(x \right) = F_{149}\! \left(x \right)+F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{12}\! \left(x \right) F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{186}\! \left(x \right)
F_{185}\! \left(x \right) = F_{29}\! \left(x \right)
F_{186}\! \left(x \right) = F_{182}\! \left(x \right)
F_{187}\! \left(x \right) = F_{174}\! \left(x \right)+F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{12}\! \left(x \right) F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{192}\! \left(x \right)
F_{191}\! \left(x \right) = F_{182}\! \left(x \right)
F_{192}\! \left(x \right) = F_{188}\! \left(x \right)
F_{193}\! \left(x \right) = F_{12}\! \left(x \right) F_{154}\! \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_38(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_14(x) + F_24(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_12(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_12(x))
Eq(F_23(x), F_19(x))
Eq(F_24(x), F_25(x) + F_26(x) + F_37(x))
Eq(F_25(x), 0)
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_10(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_10(x)*F_12(x))
Eq(F_31(x), F_24(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_29(x))
Eq(F_36(x), F_32(x))
Eq(F_37(x), F_12(x)*F_13(x))
Eq(F_38(x), F_39(x) + F_51(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_45(x))
Eq(F_42(x), F_1(x) + F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_12(x)*F_42(x))
Eq(F_45(x), F_39(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_43(x))
Eq(F_50(x), F_46(x))
Eq(F_51(x), F_146(x) + F_25(x) + F_52(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_91(x))
Eq(F_54(x), F_55(x) + F_6(x))
Eq(F_55(x), F_25(x) + F_56(x) + F_61(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_10(x) + F_58(x))
Eq(F_58(x), F_25(x) + F_56(x) + F_59(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_43(x) + F_58(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_60(x) + F_63(x))
Eq(F_63(x), F_64(x) + F_77(x))
Eq(F_64(x), F_25(x) + F_65(x) + F_68(x))
Eq(F_65(x), F_12(x)*F_66(x))
Eq(F_66(x), F_12(x) + F_67(x))
Eq(F_67(x), F_65(x))
Eq(F_68(x), F_12(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_43(x) + F_67(x))
Eq(F_71(x), F_64(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), F_67(x))
Eq(F_76(x), F_72(x))
Eq(F_77(x), F_25(x) + F_78(x) + F_81(x) + F_90(x))
Eq(F_78(x), F_12(x)*F_79(x))
Eq(F_79(x), F_29(x) + F_80(x))
Eq(F_80(x), F_78(x))
Eq(F_81(x), F_12(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_84(x))
Eq(F_83(x), F_58(x) + F_80(x))
Eq(F_84(x), F_77(x) + F_85(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_12(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_80(x))
Eq(F_89(x), F_85(x))
Eq(F_90(x), F_12(x)*F_63(x))
Eq(F_91(x), F_51(x) + F_92(x))
Eq(F_92(x), 2*F_25(x) + F_93(x) + F_97(x))
Eq(F_93(x), F_12(x)*F_94(x))
Eq(F_94(x), F_95(x) + F_96(x))
Eq(F_95(x), F_55(x))
Eq(F_96(x), F_92(x))
Eq(F_97(x), F_12(x)*F_98(x))
Eq(F_98(x), F_106(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_46(x))
Eq(F_100(x), F_101(x) + F_105(x) + 2*F_25(x))
Eq(F_101(x), F_102(x)*F_12(x))
Eq(F_102(x), F_103(x) + F_104(x))
Eq(F_103(x), F_58(x))
Eq(F_104(x), F_100(x))
Eq(F_105(x), F_12(x)*F_99(x))
Eq(F_106(x), F_107(x) + F_124(x))
Eq(F_107(x), F_108(x) + F_120(x) + 2*F_25(x))
Eq(F_108(x), F_109(x)*F_12(x))
Eq(F_109(x), F_110(x) + F_114(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x)*F_12(x))
Eq(F_113(x), F_111(x) + F_43(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_12(x))
Eq(F_117(x), F_118(x) + F_119(x))
Eq(F_118(x), F_111(x))
Eq(F_119(x), F_115(x))
Eq(F_120(x), F_12(x)*F_121(x))
Eq(F_121(x), F_122(x) + F_123(x))
Eq(F_122(x), F_46(x))
Eq(F_123(x), F_107(x))
Eq(F_124(x), F_125(x) + F_141(x) + F_145(x) + 2*F_25(x))
Eq(F_125(x), F_12(x)*F_126(x))
Eq(F_126(x), F_127(x) + F_133(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_129(x) + F_131(x) + 2*F_25(x))
Eq(F_129(x), F_12(x)*F_130(x))
Eq(F_130(x), F_128(x) + F_58(x))
Eq(F_131(x), F_12(x)*F_132(x))
Eq(F_132(x), F_111(x) + F_128(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x) + F_139(x) + 3*F_25(x))
Eq(F_135(x), F_12(x)*F_136(x))
Eq(F_136(x), F_137(x) + F_138(x))
Eq(F_137(x), F_128(x))
Eq(F_138(x), F_134(x))
Eq(F_139(x), F_12(x)*F_140(x))
Eq(F_140(x), F_115(x) + F_134(x))
Eq(F_141(x), F_12(x)*F_142(x))
Eq(F_142(x), F_143(x) + F_144(x))
Eq(F_143(x), F_100(x))
Eq(F_144(x), F_124(x))
Eq(F_145(x), F_106(x)*F_12(x))
Eq(F_146(x), F_12(x)*F_147(x))
Eq(F_147(x), F_148(x) + F_154(x))
Eq(F_148(x), F_149(x) + F_39(x))
Eq(F_149(x), F_150(x) + F_153(x) + F_25(x))
Eq(F_150(x), F_12(x)*F_151(x))
Eq(F_151(x), F_152(x) + F_57(x))
Eq(F_152(x), F_100(x) + F_149(x))
Eq(F_153(x), F_12(x)*F_148(x))
Eq(F_154(x), F_155(x) + F_174(x))
Eq(F_155(x), F_156(x) + F_160(x) + F_25(x))
Eq(F_156(x), F_12(x)*F_157(x))
Eq(F_157(x), F_158(x) + F_159(x))
Eq(F_158(x), F_111(x) + F_43(x))
Eq(F_159(x), F_115(x) + F_46(x))
Eq(F_160(x), F_12(x)*F_161(x))
Eq(F_161(x), F_162(x) + F_168(x))
Eq(F_162(x), F_163(x) + F_39(x))
Eq(F_163(x), F_164(x))
Eq(F_164(x), F_12(x)*F_165(x))
Eq(F_165(x), F_166(x) + F_167(x))
Eq(F_166(x), F_12(x))
Eq(F_167(x), F_163(x))
Eq(F_168(x), F_155(x) + F_169(x))
Eq(F_169(x), F_170(x))
Eq(F_170(x), F_12(x)*F_171(x))
Eq(F_171(x), F_172(x) + F_173(x))
Eq(F_172(x), F_163(x))
Eq(F_173(x), F_169(x))
Eq(F_174(x), F_175(x) + F_179(x) + F_193(x) + F_25(x))
Eq(F_175(x), F_12(x)*F_176(x))
Eq(F_176(x), F_177(x) + F_178(x))
Eq(F_177(x), F_128(x) + F_58(x))
Eq(F_178(x), F_100(x) + F_134(x))
Eq(F_179(x), F_12(x)*F_180(x))
Eq(F_180(x), F_181(x) + F_187(x))
Eq(F_181(x), F_149(x) + F_182(x))
Eq(F_182(x), F_183(x))
Eq(F_183(x), F_12(x)*F_184(x))
Eq(F_184(x), F_185(x) + F_186(x))
Eq(F_185(x), F_29(x))
Eq(F_186(x), F_182(x))
Eq(F_187(x), F_174(x) + F_188(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_12(x)*F_190(x))
Eq(F_190(x), F_191(x) + F_192(x))
Eq(F_191(x), F_182(x))
Eq(F_192(x), F_188(x))
Eq(F_193(x), F_12(x)*F_154(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:
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