0123_0231_0312_1230_2130
Counting sequence:
1, 1, 2, 6, 19, 58, 168, 464, 1230, 3147, 7809, 18875, 44613, 103468, 236158, 531786, 1183904, 2610321, 5708079, 12394125, 26748095, 57420762, 122696692, 261111076, 553666434, 1170232103, 2466275373, 5184188079, 10871668425, 22749941912, 47513117754, 99052730830, 206158483828, 428423048013, 889058297723, 1842541045281, 3813931042659, 7885560048486, 16286516089424, 33603824237640, 69269232675190, 142661633841667, 293569604767257, 603631883814371, 1240249116311949, 2546468930126148, 5224879255405878, 10713641301282194, 21955048183683720, 44965627529800777, 92042317384680199, 188306759419748085, 385057768140521543, 787004034883364658, 1607785066971665388, 3283124128353519276, 6701356245527756714, 13672928468697317151, 27886288892678636869, 56853441695925703255, 115868611212988720785, 236060678068252557872, 480768267421055870322, 978830357411213807766, 1992248359960632345564, 4053672010197674786693, 8245694600948170441683, 16768090363001983340809, 34089583048215252363115, 69285970740853076903742, 140785550770551299027144, 285998320118792889410640, 580851077392966362505758, 1179411029096693893409403, 2394239806814910124703153, 4859315110872864926325771, 9860301216231819207706069, 20003944421435817126804316, 40574572820815991677746414, 82282513597520698205194970, 166831763106818826111296880, 338196998037192511625989377, 685460939721494742060433887, 1389055766737208921739527261, 2814379308062856718718211279, 5701294165302591187916665738, 11547659428958937876795842788, 23385461054625386755518831924, 47351206502665795514894182610, 95862981792161635037503734807, 194047101157983358090440650589, 392736477463286892211750218495, 794757505221214136485240944473, 1608084111031708977093965698248, 3253306423241979362434901935018, 6580889248841081541363747996766, 13310331302396408715715387430724, 26917768214221308697406561057981, 54429747647299599926764697974059, 110047917732313164917432551276785, 222472680340054259962671416975475
Generating function in Maple syntax:
(x^8-2*x^7-5*x^6+25*x^5-48*x^4+48*x^3-27*x^2+8*x-1)/(2*x-1)^2/(x-1)^5
Generating function in latex syntax:
\frac{x^{8}-2 x^{7}-5 x^{6}+25 x^{5}-48 x^{4}+48 x^{3}-27 x^{2}+8 x -1}{\left(2 x -1\right)^{2} \left(x -1\right)^{5}}
Generating function in sympy syntax:
(x**8 - 2*x**7 - 5*x**6 + 25*x**5 - 48*x**4 + 48*x**3 - 27*x**2 + 8*x - 1)/((x - 1)**5*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
-(2*x-1)^2*(x-1)^5*F(x)+x^8-2*x^7-5*x^6+25*x^5-48*x^4+48*x^3-27*x^2+8*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right)^{2} \left(x -1\right)^{5} F \! \left(x \right)+x^{8}-2 x^{7}-5 x^{6}+25 x^{5}-48 x^{4}+48 x^{3}-27 x^{2}+8 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,12+35/24*n^2+29/4*n+1/4*n^3+1/24*n^4+15/8*2^n*n-12*2^n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 12+\frac{35 n^{2}}{24}+\frac{29 n}{4}+\frac{n^{3}}{4}+\frac{n^{4}}{24}+\frac{15 \,2^{n} n}{8}-12 \,2^{n} & \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) = 58
a(6) = 168
a(7) = 464
a(8) = 1230
a(n+2) = 1/24*n^4-1/12*n^3-1/24*n^2-4*a(n)+4*a(n+1)+25/12*n-1, n >= 9
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 58
a \! \left(6\right) = 168
a \! \left(7\right) = 464
a \! \left(8\right) = 1230
a \! \left(n +2\right) = \frac{n^{4}}{24}-\frac{n^{3}}{12}-\frac{n^{2}}{24}-4 a \! \left(n \right)+4 a \! \left(n +1\right)+\frac{25 n}{12}-1, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/17028/
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[17,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[11,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[11,x]+F[14,x]
F[17,x] = F[18,x]+F[2,x]
F[18,x] = F[19,x]+F[20,x]+F[258,x]
F[19,x] = 0
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[40,x]
F[22,x] = F[23,x]+F[7,x]
F[23,x] = F[19,x]+F[24,x]+F[34,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[26,x]+F[30,x]
F[26,x] = F[11,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[11,x]+F[27,x]
F[30,x] = F[14,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[27,x]+F[31,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[13,x]+F[36,x]
F[36,x] = F[27,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[14,x]+F[37,x]
F[40,x] = F[126,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[50,x]
F[44,x] = F[45,x]+F[7,x]
F[45,x] = F[46,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = F[11,x]
F[49,x] = F[14,x]
F[50,x] = F[41,x]+F[51,x]
F[51,x] = 2*F[19,x]+F[52,x]+F[74,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]+F[59,x]
F[54,x] = F[45,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[49,x]+F[58,x]
F[58,x] = F[37,x]
F[59,x] = F[60,x]+F[65,x]
F[60,x] = F[61,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = F[45,x]
F[64,x] = F[60,x]
F[65,x] = F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[55,x]
F[69,x] = F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[55,x]
F[73,x] = F[70,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[103,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[82,x]
F[80,x] = F[11,x]+F[81,x]
F[81,x] = F[46,x]
F[82,x] = F[77,x]+F[83,x]
F[83,x] = 2*F[19,x]+F[74,x]+F[84,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[86,x]+F[88,x]
F[86,x] = F[81,x]+F[87,x]
F[87,x] = F[56,x]
F[88,x] = F[89,x]+F[94,x]
F[89,x] = F[90,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[92,x]+F[93,x]
F[92,x] = F[81,x]
F[93,x] = F[89,x]
F[94,x] = F[95,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[97,x]+F[98,x]
F[97,x] = F[87,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[4,x]
F[100,x] = F[101,x]+F[102,x]
F[101,x] = F[87,x]
F[102,x] = F[99,x]
F[103,x] = F[104,x]
F[104,x] = 2*F[19,x]+F[105,x]+F[124,x]
F[105,x] = F[106,x]*F[4,x]
F[106,x] = F[107,x]+F[109,x]
F[107,x] = F[108,x]+F[14,x]
F[108,x] = F[38,x]
F[109,x] = F[110,x]+F[115,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]*F[4,x]
F[112,x] = F[113,x]+F[114,x]
F[113,x] = F[14,x]
F[114,x] = F[110,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[4,x]
F[117,x] = F[118,x]+F[119,x]
F[118,x] = F[108,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[123,x]
F[122,x] = F[108,x]
F[123,x] = F[120,x]
F[124,x] = F[125,x]*F[4,x]
F[125,x] = F[104,x]+F[77,x]
F[126,x] = 2*F[19,x]+F[127,x]+F[254,x]
F[127,x] = F[128,x]*F[4,x]
F[128,x] = F[129,x]+F[141,x]
F[129,x] = F[130,x]+F[23,x]
F[130,x] = 2*F[19,x]+F[131,x]+F[135,x]
F[131,x] = F[132,x]*F[4,x]
F[132,x] = F[133,x]+F[134,x]
F[133,x] = F[27,x]
F[134,x] = F[31,x]
F[135,x] = F[136,x]*F[4,x]
F[136,x] = F[137,x]+F[30,x]
F[137,x] = F[138,x]+F[37,x]
F[138,x] = F[139,x]
F[139,x] = F[140,x]*F[4,x]
F[140,x] = F[138,x]+F[31,x]
F[141,x] = F[142,x]+F[227,x]
F[142,x] = F[143,x]
F[143,x] = F[144,x]*F[4,x]
F[144,x] = F[145,x]+F[151,x]
F[145,x] = F[146,x]+F[23,x]
F[146,x] = F[147,x]
F[147,x] = F[148,x]*F[4,x]
F[148,x] = F[149,x]+F[150,x]
F[149,x] = F[27,x]
F[150,x] = F[31,x]
F[151,x] = F[142,x]+F[152,x]
F[152,x] = 3*F[19,x]+F[153,x]+F[175,x]
F[153,x] = F[154,x]*F[4,x]
F[154,x] = F[155,x]+F[160,x]
F[155,x] = F[146,x]+F[156,x]
F[156,x] = F[157,x]
F[157,x] = F[158,x]*F[4,x]
F[158,x] = F[150,x]+F[159,x]
F[159,x] = F[138,x]
F[160,x] = F[161,x]+F[166,x]
F[161,x] = F[162,x]
F[162,x] = F[163,x]*F[4,x]
F[163,x] = F[164,x]+F[165,x]
F[164,x] = F[146,x]
F[165,x] = F[161,x]
F[166,x] = F[167,x]
F[167,x] = F[168,x]*F[4,x]
F[168,x] = F[169,x]+F[170,x]
F[169,x] = F[156,x]
F[170,x] = F[171,x]
F[171,x] = F[172,x]*F[4,x]
F[172,x] = F[173,x]+F[174,x]
F[173,x] = F[156,x]
F[174,x] = F[171,x]
F[175,x] = F[176,x]*F[4,x]
F[176,x] = F[177,x]+F[204,x]
F[177,x] = F[178,x]
F[178,x] = F[179,x]
F[179,x] = F[180,x]*F[4,x]
F[180,x] = F[181,x]+F[183,x]
F[181,x] = F[182,x]+F[27,x]
F[182,x] = F[147,x]
F[183,x] = F[178,x]+F[184,x]
F[184,x] = 3*F[19,x]+F[175,x]+F[185,x]
F[185,x] = F[186,x]*F[4,x]
F[186,x] = F[187,x]+F[189,x]
F[187,x] = F[182,x]+F[188,x]
F[188,x] = F[157,x]
F[189,x] = F[190,x]+F[195,x]
F[190,x] = F[191,x]
F[191,x] = F[192,x]*F[4,x]
F[192,x] = F[193,x]+F[194,x]
F[193,x] = F[182,x]
F[194,x] = F[190,x]
F[195,x] = F[196,x]
F[196,x] = F[197,x]*F[4,x]
F[197,x] = F[198,x]+F[199,x]
F[198,x] = F[188,x]
F[199,x] = F[200,x]
F[200,x] = F[201,x]*F[4,x]
F[201,x] = F[202,x]+F[203,x]
F[202,x] = F[188,x]
F[203,x] = F[200,x]
F[204,x] = F[205,x]
F[205,x] = 3*F[19,x]+F[206,x]+F[225,x]
F[206,x] = F[207,x]*F[4,x]
F[207,x] = F[208,x]+F[210,x]
F[208,x] = F[209,x]+F[31,x]
F[209,x] = F[139,x]
F[210,x] = F[211,x]+F[216,x]
F[211,x] = F[212,x]
F[212,x] = F[213,x]*F[4,x]
F[213,x] = F[214,x]+F[215,x]
F[214,x] = F[31,x]
F[215,x] = F[211,x]
F[216,x] = F[217,x]
F[217,x] = F[218,x]*F[4,x]
F[218,x] = F[219,x]+F[220,x]
F[219,x] = F[209,x]
F[220,x] = F[221,x]
F[221,x] = F[222,x]*F[4,x]
F[222,x] = F[223,x]+F[224,x]
F[223,x] = F[209,x]
F[224,x] = F[221,x]
F[225,x] = F[226,x]*F[4,x]
F[226,x] = F[178,x]+F[205,x]
F[227,x] = 3*F[19,x]+F[228,x]+F[250,x]
F[228,x] = F[229,x]*F[4,x]
F[229,x] = F[230,x]+F[235,x]
F[230,x] = F[130,x]+F[231,x]
F[231,x] = F[232,x]
F[232,x] = F[233,x]*F[4,x]
F[233,x] = F[134,x]+F[234,x]
F[234,x] = F[138,x]
F[235,x] = F[236,x]+F[241,x]
F[236,x] = F[237,x]
F[237,x] = F[238,x]*F[4,x]
F[238,x] = F[239,x]+F[240,x]
F[239,x] = F[130,x]
F[240,x] = F[236,x]
F[241,x] = F[242,x]
F[242,x] = F[243,x]*F[4,x]
F[243,x] = F[244,x]+F[245,x]
F[244,x] = F[231,x]
F[245,x] = F[246,x]
F[246,x] = F[247,x]*F[4,x]
F[247,x] = F[248,x]+F[249,x]
F[248,x] = F[231,x]
F[249,x] = F[246,x]
F[250,x] = F[251,x]*F[4,x]
F[251,x] = F[252,x]+F[253,x]
F[252,x] = F[178,x]
F[253,x] = F[205,x]
F[254,x] = F[255,x]*F[4,x]
F[255,x] = F[256,x]+F[257,x]
F[256,x] = F[178,x]+F[77,x]
F[257,x] = F[104,x]+F[205,x]
F[258,x] = F[259,x]*F[4,x]
F[259,x] = F[260,x]+F[261,x]
F[260,x] = F[2,x]+F[77,x]
F[261,x] = F[104,x]+F[262,x]
F[262,x] = F[19,x]+F[263,x]+F[320,x]
F[263,x] = F[264,x]*F[4,x]
F[264,x] = F[265,x]+F[267,x]
F[265,x] = F[11,x]+F[266,x]
F[266,x] = F[19,x]+F[24,x]+F[28,x]
F[267,x] = F[268,x]+F[77,x]
F[268,x] = 2*F[19,x]+F[254,x]+F[269,x]
F[269,x] = F[270,x]*F[4,x]
F[270,x] = F[271,x]+F[273,x]
F[271,x] = F[266,x]+F[272,x]
F[272,x] = 2*F[19,x]+F[131,x]+F[135,x]
F[273,x] = F[274,x]+F[300,x]
F[274,x] = F[275,x]
F[275,x] = F[276,x]*F[4,x]
F[276,x] = F[277,x]+F[279,x]
F[277,x] = F[266,x]+F[278,x]
F[278,x] = F[147,x]
F[279,x] = F[274,x]+F[280,x]
F[280,x] = 3*F[19,x]+F[175,x]+F[281,x]
F[281,x] = F[282,x]*F[4,x]
F[282,x] = F[283,x]+F[285,x]
F[283,x] = F[278,x]+F[284,x]
F[284,x] = F[157,x]
F[285,x] = F[286,x]+F[291,x]
F[286,x] = F[287,x]
F[287,x] = F[288,x]*F[4,x]
F[288,x] = F[289,x]+F[290,x]
F[289,x] = F[278,x]
F[290,x] = F[286,x]
F[291,x] = F[292,x]
F[292,x] = F[293,x]*F[4,x]
F[293,x] = F[294,x]+F[295,x]
F[294,x] = F[284,x]
F[295,x] = F[296,x]
F[296,x] = F[297,x]*F[4,x]
F[297,x] = F[298,x]+F[299,x]
F[298,x] = F[284,x]
F[299,x] = F[296,x]
F[300,x] = 3*F[19,x]+F[250,x]+F[301,x]
F[301,x] = F[302,x]*F[4,x]
F[302,x] = F[303,x]+F[305,x]
F[303,x] = F[272,x]+F[304,x]
F[304,x] = F[232,x]
F[305,x] = F[306,x]+F[311,x]
F[306,x] = F[307,x]
F[307,x] = F[308,x]*F[4,x]
F[308,x] = F[309,x]+F[310,x]
F[309,x] = F[272,x]
F[310,x] = F[306,x]
F[311,x] = F[312,x]
F[312,x] = F[313,x]*F[4,x]
F[313,x] = F[314,x]+F[315,x]
F[314,x] = F[304,x]
F[315,x] = F[316,x]
F[316,x] = F[317,x]*F[4,x]
F[317,x] = F[318,x]+F[319,x]
F[318,x] = F[304,x]
F[319,x] = F[316,x]
F[320,x] = F[321,x]*F[4,x]
F[321,x] = F[2,x]+F[262,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_{17}\! \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_{11}\! \left(x \right)+F_{14}\! \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_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{2}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{258}\! \left(x \right)
F_{19}\! \left(x \right) = 0
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_{40}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{7}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)+F_{34}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{30}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)+F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{27}\! \left(x \right)+F_{31}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{13}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{27}\! \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_{14}\! \left(x \right)+F_{37}\! \left(x \right)
F_{40}\! \left(x \right) = F_{126}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \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_{50}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{7}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \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_{11}\! \left(x \right)
F_{49}\! \left(x \right) = F_{14}\! \left(x \right)
F_{50}\! \left(x \right) = F_{41}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{52}\! \left(x \right)+F_{74}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{59}\! \left(x \right)
F_{54}\! \left(x \right) = F_{45}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{49}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{37}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{65}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = F_{45}\! \left(x \right)
F_{64}\! \left(x \right) = F_{60}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{55}\! \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_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{55}\! \left(x \right)
F_{73}\! \left(x \right) = F_{70}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{103}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{82}\! \left(x \right)
F_{80}\! \left(x \right) = F_{11}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{46}\! \left(x \right)
F_{82}\! \left(x \right) = F_{77}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{74}\! \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_{86}\! \left(x \right)+F_{88}\! \left(x \right)
F_{86}\! \left(x \right) = F_{81}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{56}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{94}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{93}\! \left(x \right)
F_{92}\! \left(x \right) = F_{81}\! \left(x \right)
F_{93}\! \left(x \right) = F_{89}\! \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_{98}\! \left(x \right)
F_{97}\! \left(x \right) = F_{87}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{4}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{102}\! \left(x \right)
F_{101}\! \left(x \right) = F_{87}\! \left(x \right)
F_{102}\! \left(x \right) = F_{99}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{105}\! \left(x \right)+F_{124}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{109}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{14}\! \left(x \right)
F_{108}\! \left(x \right) = F_{38}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{115}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{4}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{114}\! \left(x \right)
F_{113}\! \left(x \right) = F_{14}\! \left(x \right)
F_{114}\! \left(x \right) = F_{110}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \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_{119}\! \left(x \right)
F_{118}\! \left(x \right) = F_{108}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{123}\! \left(x \right)
F_{122}\! \left(x \right) = F_{108}\! \left(x \right)
F_{123}\! \left(x \right) = F_{120}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{4}\! \left(x \right)
F_{125}\! \left(x \right) = F_{104}\! \left(x \right)+F_{77}\! \left(x \right)
F_{126}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{127}\! \left(x \right)+F_{254}\! \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_{141}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{23}\! \left(x \right)
F_{130}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{131}\! \left(x \right)+F_{135}\! \left(x \right)
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_{134}\! \left(x \right)
F_{133}\! \left(x \right) = F_{27}\! \left(x \right)
F_{134}\! \left(x \right) = F_{31}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{30}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{37}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{4}\! \left(x \right)
F_{140}\! \left(x \right) = F_{138}\! \left(x \right)+F_{31}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{227}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right) F_{4}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{151}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{23}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{4}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{150}\! \left(x \right)
F_{149}\! \left(x \right) = F_{27}\! \left(x \right)
F_{150}\! \left(x \right) = F_{31}\! \left(x \right)
F_{151}\! \left(x \right) = F_{142}\! \left(x \right)+F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = 3 F_{19}\! \left(x \right)+F_{153}\! \left(x \right)+F_{175}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right) F_{4}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{160}\! \left(x \right)
F_{155}\! \left(x \right) = F_{146}\! \left(x \right)+F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right) F_{4}\! \left(x \right)
F_{158}\! \left(x \right) = F_{150}\! \left(x \right)+F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{138}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{166}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right) F_{4}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)+F_{165}\! \left(x \right)
F_{164}\! \left(x \right) = F_{146}\! \left(x \right)
F_{165}\! \left(x \right) = F_{161}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right) F_{4}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{170}\! \left(x \right)
F_{169}\! \left(x \right) = F_{156}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right) F_{4}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)+F_{174}\! \left(x \right)
F_{173}\! \left(x \right) = F_{156}\! \left(x \right)
F_{174}\! \left(x \right) = F_{171}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right) F_{4}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)+F_{204}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right) F_{4}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{183}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{27}\! \left(x \right)
F_{182}\! \left(x \right) = F_{147}\! \left(x \right)
F_{183}\! \left(x \right) = F_{178}\! \left(x \right)+F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = 3 F_{19}\! \left(x \right)+F_{175}\! \left(x \right)+F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right) F_{4}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)+F_{189}\! \left(x \right)
F_{187}\! \left(x \right) = F_{182}\! \left(x \right)+F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = F_{157}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)+F_{195}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right) F_{4}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{194}\! \left(x \right)
F_{193}\! \left(x \right) = F_{182}\! \left(x \right)
F_{194}\! \left(x \right) = F_{190}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right) F_{4}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)+F_{199}\! \left(x \right)
F_{198}\! \left(x \right) = F_{188}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right) F_{4}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)+F_{203}\! \left(x \right)
F_{202}\! \left(x \right) = F_{188}\! \left(x \right)
F_{203}\! \left(x \right) = F_{200}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right)
F_{205}\! \left(x \right) = 3 F_{19}\! \left(x \right)+F_{206}\! \left(x \right)+F_{225}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right) F_{4}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)+F_{210}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)+F_{31}\! \left(x \right)
F_{209}\! \left(x \right) = F_{139}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)+F_{216}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right) F_{4}\! \left(x \right)
F_{213}\! \left(x \right) = F_{214}\! \left(x \right)+F_{215}\! \left(x \right)
F_{214}\! \left(x \right) = F_{31}\! \left(x \right)
F_{215}\! \left(x \right) = F_{211}\! \left(x \right)
F_{216}\! \left(x \right) = F_{217}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right) F_{4}\! \left(x \right)
F_{218}\! \left(x \right) = F_{219}\! \left(x \right)+F_{220}\! \left(x \right)
F_{219}\! \left(x \right) = F_{209}\! \left(x \right)
F_{220}\! \left(x \right) = F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right) F_{4}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right)+F_{224}\! \left(x \right)
F_{223}\! \left(x \right) = F_{209}\! \left(x \right)
F_{224}\! \left(x \right) = F_{221}\! \left(x \right)
F_{225}\! \left(x \right) = F_{226}\! \left(x \right) F_{4}\! \left(x \right)
F_{226}\! \left(x \right) = F_{178}\! \left(x \right)+F_{205}\! \left(x \right)
F_{227}\! \left(x \right) = 3 F_{19}\! \left(x \right)+F_{228}\! \left(x \right)+F_{250}\! \left(x \right)
F_{228}\! \left(x \right) = F_{229}\! \left(x \right) F_{4}\! \left(x \right)
F_{229}\! \left(x \right) = F_{230}\! \left(x \right)+F_{235}\! \left(x \right)
F_{230}\! \left(x \right) = F_{130}\! \left(x \right)+F_{231}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right) F_{4}\! \left(x \right)
F_{233}\! \left(x \right) = F_{134}\! \left(x \right)+F_{234}\! \left(x \right)
F_{234}\! \left(x \right) = F_{138}\! \left(x \right)
F_{235}\! \left(x \right) = F_{236}\! \left(x \right)+F_{241}\! \left(x \right)
F_{236}\! \left(x \right) = F_{237}\! \left(x \right)
F_{237}\! \left(x \right) = F_{238}\! \left(x \right) F_{4}\! \left(x \right)
F_{238}\! \left(x \right) = F_{239}\! \left(x \right)+F_{240}\! \left(x \right)
F_{239}\! \left(x \right) = F_{130}\! \left(x \right)
F_{240}\! \left(x \right) = F_{236}\! \left(x \right)
F_{241}\! \left(x \right) = F_{242}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x \right) F_{4}\! \left(x \right)
F_{243}\! \left(x \right) = F_{244}\! \left(x \right)+F_{245}\! \left(x \right)
F_{244}\! \left(x \right) = F_{231}\! \left(x \right)
F_{245}\! \left(x \right) = F_{246}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right) F_{4}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right)+F_{249}\! \left(x \right)
F_{248}\! \left(x \right) = F_{231}\! \left(x \right)
F_{249}\! \left(x \right) = F_{246}\! \left(x \right)
F_{250}\! \left(x \right) = F_{251}\! \left(x \right) F_{4}\! \left(x \right)
F_{251}\! \left(x \right) = F_{252}\! \left(x \right)+F_{253}\! \left(x \right)
F_{252}\! \left(x \right) = F_{178}\! \left(x \right)
F_{253}\! \left(x \right) = F_{205}\! \left(x \right)
F_{254}\! \left(x \right) = F_{255}\! \left(x \right) F_{4}\! \left(x \right)
F_{255}\! \left(x \right) = F_{256}\! \left(x \right)+F_{257}\! \left(x \right)
F_{256}\! \left(x \right) = F_{178}\! \left(x \right)+F_{77}\! \left(x \right)
F_{257}\! \left(x \right) = F_{104}\! \left(x \right)+F_{205}\! \left(x \right)
F_{258}\! \left(x \right) = F_{259}\! \left(x \right) F_{4}\! \left(x \right)
F_{259}\! \left(x \right) = F_{260}\! \left(x \right)+F_{261}\! \left(x \right)
F_{260}\! \left(x \right) = F_{2}\! \left(x \right)+F_{77}\! \left(x \right)
F_{261}\! \left(x \right) = F_{104}\! \left(x \right)+F_{262}\! \left(x \right)
F_{262}\! \left(x \right) = F_{19}\! \left(x \right)+F_{263}\! \left(x \right)+F_{320}\! \left(x \right)
F_{263}\! \left(x \right) = F_{264}\! \left(x \right) F_{4}\! \left(x \right)
F_{264}\! \left(x \right) = F_{265}\! \left(x \right)+F_{267}\! \left(x \right)
F_{265}\! \left(x \right) = F_{11}\! \left(x \right)+F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)+F_{28}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right)+F_{77}\! \left(x \right)
F_{268}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{254}\! \left(x \right)+F_{269}\! \left(x \right)
F_{269}\! \left(x \right) = F_{270}\! \left(x \right) F_{4}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right)+F_{273}\! \left(x \right)
F_{271}\! \left(x \right) = F_{266}\! \left(x \right)+F_{272}\! \left(x \right)
F_{272}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{131}\! \left(x \right)+F_{135}\! \left(x \right)
F_{273}\! \left(x \right) = F_{274}\! \left(x \right)+F_{300}\! \left(x \right)
F_{274}\! \left(x \right) = F_{275}\! \left(x \right)
F_{275}\! \left(x \right) = F_{276}\! \left(x \right) F_{4}\! \left(x \right)
F_{276}\! \left(x \right) = F_{277}\! \left(x \right)+F_{279}\! \left(x \right)
F_{277}\! \left(x \right) = F_{266}\! \left(x \right)+F_{278}\! \left(x \right)
F_{278}\! \left(x \right) = F_{147}\! \left(x \right)
F_{279}\! \left(x \right) = F_{274}\! \left(x \right)+F_{280}\! \left(x \right)
F_{280}\! \left(x \right) = 3 F_{19}\! \left(x \right)+F_{175}\! \left(x \right)+F_{281}\! \left(x \right)
F_{281}\! \left(x \right) = F_{282}\! \left(x \right) F_{4}\! \left(x \right)
F_{282}\! \left(x \right) = F_{283}\! \left(x \right)+F_{285}\! \left(x \right)
F_{283}\! \left(x \right) = F_{278}\! \left(x \right)+F_{284}\! \left(x \right)
F_{284}\! \left(x \right) = F_{157}\! \left(x \right)
F_{285}\! \left(x \right) = F_{286}\! \left(x \right)+F_{291}\! \left(x \right)
F_{286}\! \left(x \right) = F_{287}\! \left(x \right)
F_{287}\! \left(x \right) = F_{288}\! \left(x \right) F_{4}\! \left(x \right)
F_{288}\! \left(x \right) = F_{289}\! \left(x \right)+F_{290}\! \left(x \right)
F_{289}\! \left(x \right) = F_{278}\! \left(x \right)
F_{290}\! \left(x \right) = F_{286}\! \left(x \right)
F_{291}\! \left(x \right) = F_{292}\! \left(x \right)
F_{292}\! \left(x \right) = F_{293}\! \left(x \right) F_{4}\! \left(x \right)
F_{293}\! \left(x \right) = F_{294}\! \left(x \right)+F_{295}\! \left(x \right)
F_{294}\! \left(x \right) = F_{284}\! \left(x \right)
F_{295}\! \left(x \right) = F_{296}\! \left(x \right)
F_{296}\! \left(x \right) = F_{297}\! \left(x \right) F_{4}\! \left(x \right)
F_{297}\! \left(x \right) = F_{298}\! \left(x \right)+F_{299}\! \left(x \right)
F_{298}\! \left(x \right) = F_{284}\! \left(x \right)
F_{299}\! \left(x \right) = F_{296}\! \left(x \right)
F_{300}\! \left(x \right) = 3 F_{19}\! \left(x \right)+F_{250}\! \left(x \right)+F_{301}\! \left(x \right)
F_{301}\! \left(x \right) = F_{302}\! \left(x \right) F_{4}\! \left(x \right)
F_{302}\! \left(x \right) = F_{303}\! \left(x \right)+F_{305}\! \left(x \right)
F_{303}\! \left(x \right) = F_{272}\! \left(x \right)+F_{304}\! \left(x \right)
F_{304}\! \left(x \right) = F_{232}\! \left(x \right)
F_{305}\! \left(x \right) = F_{306}\! \left(x \right)+F_{311}\! \left(x \right)
F_{306}\! \left(x \right) = F_{307}\! \left(x \right)
F_{307}\! \left(x \right) = F_{308}\! \left(x \right) F_{4}\! \left(x \right)
F_{308}\! \left(x \right) = F_{309}\! \left(x \right)+F_{310}\! \left(x \right)
F_{309}\! \left(x \right) = F_{272}\! \left(x \right)
F_{310}\! \left(x \right) = F_{306}\! \left(x \right)
F_{311}\! \left(x \right) = F_{312}\! \left(x \right)
F_{312}\! \left(x \right) = F_{313}\! \left(x \right) F_{4}\! \left(x \right)
F_{313}\! \left(x \right) = F_{314}\! \left(x \right)+F_{315}\! \left(x \right)
F_{314}\! \left(x \right) = F_{304}\! \left(x \right)
F_{315}\! \left(x \right) = F_{316}\! \left(x \right)
F_{316}\! \left(x \right) = F_{317}\! \left(x \right) F_{4}\! \left(x \right)
F_{317}\! \left(x \right) = F_{318}\! \left(x \right)+F_{319}\! \left(x \right)
F_{318}\! \left(x \right) = F_{304}\! \left(x \right)
F_{319}\! \left(x \right) = F_{316}\! \left(x \right)
F_{320}\! \left(x \right) = F_{321}\! \left(x \right) F_{4}\! \left(x \right)
F_{321}\! \left(x \right) = F_{2}\! \left(x \right)+F_{262}\! \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_17(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_11(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_11(x) + F_14(x))
Eq(F_17(x), F_18(x) + F_2(x))
Eq(F_18(x), F_19(x) + F_20(x) + F_258(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_40(x))
Eq(F_22(x), F_23(x) + F_7(x))
Eq(F_23(x), F_19(x) + F_24(x) + F_34(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_26(x) + F_30(x))
Eq(F_26(x), F_11(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_11(x) + F_27(x))
Eq(F_30(x), F_14(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_27(x) + F_31(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_13(x) + F_36(x))
Eq(F_36(x), F_27(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_14(x) + F_37(x))
Eq(F_40(x), F_126(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_50(x))
Eq(F_44(x), F_45(x) + F_7(x))
Eq(F_45(x), F_46(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_11(x))
Eq(F_49(x), F_14(x))
Eq(F_50(x), F_41(x) + F_51(x))
Eq(F_51(x), 2*F_19(x) + F_52(x) + F_74(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_59(x))
Eq(F_54(x), F_45(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_49(x) + F_58(x))
Eq(F_58(x), F_37(x))
Eq(F_59(x), F_60(x) + F_65(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), F_45(x))
Eq(F_64(x), F_60(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_55(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_55(x))
Eq(F_73(x), F_70(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_103(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_82(x))
Eq(F_80(x), F_11(x) + F_81(x))
Eq(F_81(x), F_46(x))
Eq(F_82(x), F_77(x) + F_83(x))
Eq(F_83(x), 2*F_19(x) + F_74(x) + F_84(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_88(x))
Eq(F_86(x), F_81(x) + F_87(x))
Eq(F_87(x), F_56(x))
Eq(F_88(x), F_89(x) + F_94(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_93(x))
Eq(F_92(x), F_81(x))
Eq(F_93(x), F_89(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_98(x))
Eq(F_97(x), F_87(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_4(x))
Eq(F_100(x), F_101(x) + F_102(x))
Eq(F_101(x), F_87(x))
Eq(F_102(x), F_99(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x) + F_124(x) + 2*F_19(x))
Eq(F_105(x), F_106(x)*F_4(x))
Eq(F_106(x), F_107(x) + F_109(x))
Eq(F_107(x), F_108(x) + F_14(x))
Eq(F_108(x), F_38(x))
Eq(F_109(x), F_110(x) + F_115(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x)*F_4(x))
Eq(F_112(x), F_113(x) + F_114(x))
Eq(F_113(x), F_14(x))
Eq(F_114(x), F_110(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_4(x))
Eq(F_117(x), F_118(x) + F_119(x))
Eq(F_118(x), F_108(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x)*F_4(x))
Eq(F_121(x), F_122(x) + F_123(x))
Eq(F_122(x), F_108(x))
Eq(F_123(x), F_120(x))
Eq(F_124(x), F_125(x)*F_4(x))
Eq(F_125(x), F_104(x) + F_77(x))
Eq(F_126(x), F_127(x) + 2*F_19(x) + F_254(x))
Eq(F_127(x), F_128(x)*F_4(x))
Eq(F_128(x), F_129(x) + F_141(x))
Eq(F_129(x), F_130(x) + F_23(x))
Eq(F_130(x), F_131(x) + F_135(x) + 2*F_19(x))
Eq(F_131(x), F_132(x)*F_4(x))
Eq(F_132(x), F_133(x) + F_134(x))
Eq(F_133(x), F_27(x))
Eq(F_134(x), F_31(x))
Eq(F_135(x), F_136(x)*F_4(x))
Eq(F_136(x), F_137(x) + F_30(x))
Eq(F_137(x), F_138(x) + F_37(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_140(x)*F_4(x))
Eq(F_140(x), F_138(x) + F_31(x))
Eq(F_141(x), F_142(x) + F_227(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_144(x)*F_4(x))
Eq(F_144(x), F_145(x) + F_151(x))
Eq(F_145(x), F_146(x) + F_23(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_148(x)*F_4(x))
Eq(F_148(x), F_149(x) + F_150(x))
Eq(F_149(x), F_27(x))
Eq(F_150(x), F_31(x))
Eq(F_151(x), F_142(x) + F_152(x))
Eq(F_152(x), F_153(x) + F_175(x) + 3*F_19(x))
Eq(F_153(x), F_154(x)*F_4(x))
Eq(F_154(x), F_155(x) + F_160(x))
Eq(F_155(x), F_146(x) + F_156(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_158(x)*F_4(x))
Eq(F_158(x), F_150(x) + F_159(x))
Eq(F_159(x), F_138(x))
Eq(F_160(x), F_161(x) + F_166(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_163(x)*F_4(x))
Eq(F_163(x), F_164(x) + F_165(x))
Eq(F_164(x), F_146(x))
Eq(F_165(x), F_161(x))
Eq(F_166(x), F_167(x))
Eq(F_167(x), F_168(x)*F_4(x))
Eq(F_168(x), F_169(x) + F_170(x))
Eq(F_169(x), F_156(x))
Eq(F_170(x), F_171(x))
Eq(F_171(x), F_172(x)*F_4(x))
Eq(F_172(x), F_173(x) + F_174(x))
Eq(F_173(x), F_156(x))
Eq(F_174(x), F_171(x))
Eq(F_175(x), F_176(x)*F_4(x))
Eq(F_176(x), F_177(x) + F_204(x))
Eq(F_177(x), F_178(x))
Eq(F_178(x), F_179(x))
Eq(F_179(x), F_180(x)*F_4(x))
Eq(F_180(x), F_181(x) + F_183(x))
Eq(F_181(x), F_182(x) + F_27(x))
Eq(F_182(x), F_147(x))
Eq(F_183(x), F_178(x) + F_184(x))
Eq(F_184(x), F_175(x) + F_185(x) + 3*F_19(x))
Eq(F_185(x), F_186(x)*F_4(x))
Eq(F_186(x), F_187(x) + F_189(x))
Eq(F_187(x), F_182(x) + F_188(x))
Eq(F_188(x), F_157(x))
Eq(F_189(x), F_190(x) + F_195(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), F_192(x)*F_4(x))
Eq(F_192(x), F_193(x) + F_194(x))
Eq(F_193(x), F_182(x))
Eq(F_194(x), F_190(x))
Eq(F_195(x), F_196(x))
Eq(F_196(x), F_197(x)*F_4(x))
Eq(F_197(x), F_198(x) + F_199(x))
Eq(F_198(x), F_188(x))
Eq(F_199(x), F_200(x))
Eq(F_200(x), F_201(x)*F_4(x))
Eq(F_201(x), F_202(x) + F_203(x))
Eq(F_202(x), F_188(x))
Eq(F_203(x), F_200(x))
Eq(F_204(x), F_205(x))
Eq(F_205(x), 3*F_19(x) + F_206(x) + F_225(x))
Eq(F_206(x), F_207(x)*F_4(x))
Eq(F_207(x), F_208(x) + F_210(x))
Eq(F_208(x), F_209(x) + F_31(x))
Eq(F_209(x), F_139(x))
Eq(F_210(x), F_211(x) + F_216(x))
Eq(F_211(x), F_212(x))
Eq(F_212(x), F_213(x)*F_4(x))
Eq(F_213(x), F_214(x) + F_215(x))
Eq(F_214(x), F_31(x))
Eq(F_215(x), F_211(x))
Eq(F_216(x), F_217(x))
Eq(F_217(x), F_218(x)*F_4(x))
Eq(F_218(x), F_219(x) + F_220(x))
Eq(F_219(x), F_209(x))
Eq(F_220(x), F_221(x))
Eq(F_221(x), F_222(x)*F_4(x))
Eq(F_222(x), F_223(x) + F_224(x))
Eq(F_223(x), F_209(x))
Eq(F_224(x), F_221(x))
Eq(F_225(x), F_226(x)*F_4(x))
Eq(F_226(x), F_178(x) + F_205(x))
Eq(F_227(x), 3*F_19(x) + F_228(x) + F_250(x))
Eq(F_228(x), F_229(x)*F_4(x))
Eq(F_229(x), F_230(x) + F_235(x))
Eq(F_230(x), F_130(x) + F_231(x))
Eq(F_231(x), F_232(x))
Eq(F_232(x), F_233(x)*F_4(x))
Eq(F_233(x), F_134(x) + F_234(x))
Eq(F_234(x), F_138(x))
Eq(F_235(x), F_236(x) + F_241(x))
Eq(F_236(x), F_237(x))
Eq(F_237(x), F_238(x)*F_4(x))
Eq(F_238(x), F_239(x) + F_240(x))
Eq(F_239(x), F_130(x))
Eq(F_240(x), F_236(x))
Eq(F_241(x), F_242(x))
Eq(F_242(x), F_243(x)*F_4(x))
Eq(F_243(x), F_244(x) + F_245(x))
Eq(F_244(x), F_231(x))
Eq(F_245(x), F_246(x))
Eq(F_246(x), F_247(x)*F_4(x))
Eq(F_247(x), F_248(x) + F_249(x))
Eq(F_248(x), F_231(x))
Eq(F_249(x), F_246(x))
Eq(F_250(x), F_251(x)*F_4(x))
Eq(F_251(x), F_252(x) + F_253(x))
Eq(F_252(x), F_178(x))
Eq(F_253(x), F_205(x))
Eq(F_254(x), F_255(x)*F_4(x))
Eq(F_255(x), F_256(x) + F_257(x))
Eq(F_256(x), F_178(x) + F_77(x))
Eq(F_257(x), F_104(x) + F_205(x))
Eq(F_258(x), F_259(x)*F_4(x))
Eq(F_259(x), F_260(x) + F_261(x))
Eq(F_260(x), F_2(x) + F_77(x))
Eq(F_261(x), F_104(x) + F_262(x))
Eq(F_262(x), F_19(x) + F_263(x) + F_320(x))
Eq(F_263(x), F_264(x)*F_4(x))
Eq(F_264(x), F_265(x) + F_267(x))
Eq(F_265(x), F_11(x) + F_266(x))
Eq(F_266(x), F_19(x) + F_24(x) + F_28(x))
Eq(F_267(x), F_268(x) + F_77(x))
Eq(F_268(x), 2*F_19(x) + F_254(x) + F_269(x))
Eq(F_269(x), F_270(x)*F_4(x))
Eq(F_270(x), F_271(x) + F_273(x))
Eq(F_271(x), F_266(x) + F_272(x))
Eq(F_272(x), F_131(x) + F_135(x) + 2*F_19(x))
Eq(F_273(x), F_274(x) + F_300(x))
Eq(F_274(x), F_275(x))
Eq(F_275(x), F_276(x)*F_4(x))
Eq(F_276(x), F_277(x) + F_279(x))
Eq(F_277(x), F_266(x) + F_278(x))
Eq(F_278(x), F_147(x))
Eq(F_279(x), F_274(x) + F_280(x))
Eq(F_280(x), F_175(x) + 3*F_19(x) + F_281(x))
Eq(F_281(x), F_282(x)*F_4(x))
Eq(F_282(x), F_283(x) + F_285(x))
Eq(F_283(x), F_278(x) + F_284(x))
Eq(F_284(x), F_157(x))
Eq(F_285(x), F_286(x) + F_291(x))
Eq(F_286(x), F_287(x))
Eq(F_287(x), F_288(x)*F_4(x))
Eq(F_288(x), F_289(x) + F_290(x))
Eq(F_289(x), F_278(x))
Eq(F_290(x), F_286(x))
Eq(F_291(x), F_292(x))
Eq(F_292(x), F_293(x)*F_4(x))
Eq(F_293(x), F_294(x) + F_295(x))
Eq(F_294(x), F_284(x))
Eq(F_295(x), F_296(x))
Eq(F_296(x), F_297(x)*F_4(x))
Eq(F_297(x), F_298(x) + F_299(x))
Eq(F_298(x), F_284(x))
Eq(F_299(x), F_296(x))
Eq(F_300(x), 3*F_19(x) + F_250(x) + F_301(x))
Eq(F_301(x), F_302(x)*F_4(x))
Eq(F_302(x), F_303(x) + F_305(x))
Eq(F_303(x), F_272(x) + F_304(x))
Eq(F_304(x), F_232(x))
Eq(F_305(x), F_306(x) + F_311(x))
Eq(F_306(x), F_307(x))
Eq(F_307(x), F_308(x)*F_4(x))
Eq(F_308(x), F_309(x) + F_310(x))
Eq(F_309(x), F_272(x))
Eq(F_310(x), F_306(x))
Eq(F_311(x), F_312(x))
Eq(F_312(x), F_313(x)*F_4(x))
Eq(F_313(x), F_314(x) + F_315(x))
Eq(F_314(x), F_304(x))
Eq(F_315(x), F_316(x))
Eq(F_316(x), F_317(x)*F_4(x))
Eq(F_317(x), F_318(x) + F_319(x))
Eq(F_318(x), F_304(x))
Eq(F_319(x), F_316(x))
Eq(F_320(x), F_321(x)*F_4(x))
Eq(F_321(x), F_2(x) + F_262(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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