0123_1302_2130
Counting sequence:
1, 1, 2, 6, 21, 72, 230, 689, 1970, 5460, 14833, 39790, 105890, 280367, 739878, 1948186, 5121973, 13451620, 35299782, 92580429, 242705586, 636062896, 1666534337, 4365640346, 11434584546, 29946505947, 78421715110, 205352199014, 537701996645, 1407888015200, 3686230491718, 9651340338985, 25268864276050, 66157399982732, 173207630650353, 453474081914886, 1187231794976578, 3108255662767495, 8137603912818182, 21304693514657394, 55776751509079221, 146026110768413916, 382302680307811622, 1000884129178299461, 2620354105273622546, 6860186982735616872, 17960224435119300865, 47020521506994404914, 123101410454608123970, 322283850594318356915, 843750422803323694278, 2208967980765606186430, 5783154645393401749285, 15140498207214412790872, 39638344479849464040678, 103774544239533234121761, 271685306253148747859058, 711281410548710028474820, 1862158997450575375551857, 4875195725918204174098334, 12763428468534413298519906, 33415090256145788024953311, 87481843452824455383258982, 229030442408170587338593226, 599609488383373325059988021, 1569798031965321424696229972, 4109784625959335022738340870, 10759555882806171790937987389, 28168883096246156644913923570, 73747093553506250733480296480, 193072397859420500734879896513, 505470100615051061829865154250, 1323337905166324305472126983970, 3464543617245105096021338523787, 9070292951291357465461533925478, 23746335246073700266102553809686, 62168712805819209264324708493413, 162759803209162859389828733520720, 426110696897227232631075815634182, 1115572287633634565955227360372249, 2920606166305907920138263559317266, 7646246211888552104266877905096956, 20018132470568674212276999330850417, 52408151202235322171793378437043766, 137206321140972995581561652679289346, 359210812230355071129808612998664247, 940426115569435030921698253112199750, 2462067534516635647862954279928737314, 6445776488057843165122500853855419445, 16875261929811636352415220816000131020, 44180009301686550901944506662869981798, 115664765975866986373060989310059611445, 302814288627152348256523841542208219730, 792778099908065938475081295866363547352, 2075520011101997227325861567156479178753, 5433781933407829263816786447802267250786, 14225825789141297604753063860648708838018, 37243695434055677631699537302940631524195, 97505260513104963452859812385766729979782, 255272086105417669051908428529546646620014, 668310997803464956352922530553247385995301
Generating function in Maple syntax:
-(3*x^6-21*x^5+40*x^4-43*x^3+26*x^2-8*x+1)/(2*x-1)/(x^2-3*x+1)/(x-1)^4
Generating function in latex syntax:
-\frac{3 x^{6}-21 x^{5}+40 x^{4}-43 x^{3}+26 x^{2}-8 x +1}{\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x -1\right)^{4}}
Generating function in sympy syntax:
(-3*x**6 + 21*x**5 - 40*x**4 + 43*x**3 - 26*x**2 + 8*x - 1)/((x - 1)**4*(2*x - 1)*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x^2-3*x+1)*(x-1)^4*F(x)+3*x^6-21*x^5+40*x^4-43*x^3+26*x^2-8*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x -1\right)^{4} F \! \left(x \right)+3 x^{6}-21 x^{5}+40 x^{4}-43 x^{3}+26 x^{2}-8 x +1 = 0
Explicit closed form in Maple syntax:
1/30*(21*5^(1/2)-15)*(3/2-1/2*5^(1/2))^(-n)+1/30*(-21*5^(1/2)-15)*(3/2+1/2*5^(1/2))^(-n)-1/3*n^3+n^2-8/3*n-2^n+3
Explicit closed form in latex syntax:
\frac{\left(21 \sqrt{5}-15\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{30}+\frac{\left(-21 \sqrt{5}-15\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{30}-\frac{n^{3}}{3}+n^{2}-\frac{8 n}{3}-2^{n}+3
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 72
a(6) = 230
a(n+3) = -1/3*n^3+n^2+2*a(n)-7*a(n+1)+5*a(n+2)+4/3*n+1, n >= 7
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) = 72
a \! \left(6\right) = 230
a \! \left(n +3\right) = -\frac{n^{3}}{3}+n^{2}+2 a \! \left(n \right)-7 a \! \left(n +1\right)+5 a \! \left(n +2\right)+\frac{4 n}{3}+1, \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14674/
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[41,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[7,x]
F[14,x] = F[15,x]+F[16,x]+F[38,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[22,x]
F[18,x] = F[11,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[11,x]+F[19,x]
F[22,x] = F[23,x]+F[28,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[26,x]+F[27,x]
F[26,x] = F[11,x]
F[27,x] = F[23,x]
F[28,x] = F[29,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[19,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[19,x]
F[37,x] = F[33,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[7,x]
F[40,x] = F[38,x]
F[41,x] = F[2,x]+F[42,x]
F[42,x] = F[15,x]+F[273,x]+F[43,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]+F[68,x]
F[45,x] = F[46,x]+F[7,x]
F[46,x] = F[15,x]+F[16,x]+F[47,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[13,x]+F[49,x]
F[49,x] = F[50,x]+F[58,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[39,x]+F[53,x]
F[53,x] = F[50,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[50,x]+F[57,x]
F[57,x] = F[55,x]
F[58,x] = 2*F[15,x]+F[55,x]+F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[23,x]
F[62,x] = F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[23,x]
F[67,x] = F[63,x]
F[68,x] = F[132,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[72,x]+F[74,x]
F[72,x] = F[7,x]+F[73,x]
F[73,x] = F[24,x]
F[74,x] = F[69,x]+F[75,x]
F[75,x] = 2*F[15,x]+F[76,x]+F[98,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[78,x]+F[83,x]
F[78,x] = F[73,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[4,x]*F[81,x]
F[81,x] = F[27,x]+F[82,x]
F[82,x] = F[63,x]
F[83,x] = F[84,x]+F[89,x]
F[84,x] = F[85,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[87,x]+F[88,x]
F[87,x] = F[73,x]
F[88,x] = F[84,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[79,x]
F[93,x] = F[94,x]
F[94,x] = F[4,x]*F[95,x]
F[95,x] = F[96,x]+F[97,x]
F[96,x] = F[79,x]
F[97,x] = F[94,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[126,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[4,x]
F[103,x] = F[104,x]+F[105,x]
F[104,x] = F[11,x]+F[23,x]
F[105,x] = F[101,x]+F[106,x]
F[106,x] = 2*F[15,x]+F[107,x]+F[98,x]
F[107,x] = F[108,x]*F[4,x]
F[108,x] = F[109,x]+F[111,x]
F[109,x] = F[110,x]+F[23,x]
F[110,x] = F[80,x]
F[111,x] = F[112,x]+F[117,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]*F[4,x]
F[114,x] = F[115,x]+F[116,x]
F[115,x] = F[23,x]
F[116,x] = F[112,x]
F[117,x] = F[118,x]
F[118,x] = F[119,x]*F[4,x]
F[119,x] = F[120,x]+F[121,x]
F[120,x] = F[110,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x]*F[4,x]
F[123,x] = F[124,x]+F[125,x]
F[124,x] = F[110,x]
F[125,x] = F[122,x]
F[126,x] = F[127,x]
F[127,x] = F[128,x]
F[128,x] = F[129,x]*F[4,x]
F[129,x] = F[130,x]+F[131,x]
F[130,x] = F[101,x]
F[131,x] = F[127,x]
F[132,x] = 2*F[15,x]+F[133,x]+F[239,x]
F[133,x] = F[134,x]*F[4,x]
F[134,x] = F[135,x]+F[149,x]
F[135,x] = F[136,x]+F[46,x]
F[136,x] = 2*F[15,x]+F[137,x]+F[29,x]
F[137,x] = F[138,x]*F[4,x]
F[138,x] = F[139,x]+F[22,x]
F[139,x] = F[140,x]+F[63,x]
F[140,x] = F[141,x]
F[141,x] = F[142,x]*F[4,x]
F[142,x] = F[143,x]+F[144,x]
F[143,x] = F[33,x]
F[144,x] = F[145,x]
F[145,x] = F[146,x]*F[4,x]
F[146,x] = F[147,x]+F[148,x]
F[147,x] = F[33,x]
F[148,x] = F[145,x]
F[149,x] = F[150,x]+F[212,x]
F[150,x] = F[151,x]
F[151,x] = F[152,x]*F[4,x]
F[152,x] = F[153,x]+F[155,x]
F[153,x] = F[154,x]+F[46,x]
F[154,x] = F[34,x]
F[155,x] = F[150,x]+F[156,x]
F[156,x] = 3*F[15,x]+F[157,x]+F[179,x]
F[157,x] = F[158,x]*F[4,x]
F[158,x] = F[159,x]+F[164,x]
F[159,x] = F[154,x]+F[160,x]
F[160,x] = F[161,x]
F[161,x] = F[162,x]*F[4,x]
F[162,x] = F[163,x]+F[37,x]
F[163,x] = F[145,x]
F[164,x] = F[165,x]+F[170,x]
F[165,x] = F[166,x]
F[166,x] = F[167,x]*F[4,x]
F[167,x] = F[168,x]+F[169,x]
F[168,x] = F[154,x]
F[169,x] = F[165,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[160,x]
F[174,x] = F[175,x]
F[175,x] = F[176,x]*F[4,x]
F[176,x] = F[177,x]+F[178,x]
F[177,x] = F[160,x]
F[178,x] = F[175,x]
F[179,x] = F[180,x]*F[4,x]
F[180,x] = F[181,x]+F[207,x]
F[181,x] = F[182,x]
F[182,x] = F[183,x]
F[183,x] = F[184,x]*F[4,x]
F[184,x] = F[185,x]+F[186,x]
F[185,x] = F[19,x]+F[33,x]
F[186,x] = F[182,x]+F[187,x]
F[187,x] = 3*F[15,x]+F[179,x]+F[188,x]
F[188,x] = F[189,x]*F[4,x]
F[189,x] = F[190,x]+F[192,x]
F[190,x] = F[191,x]+F[33,x]
F[191,x] = F[161,x]
F[192,x] = F[193,x]+F[198,x]
F[193,x] = F[194,x]
F[194,x] = F[195,x]*F[4,x]
F[195,x] = F[196,x]+F[197,x]
F[196,x] = F[33,x]
F[197,x] = F[193,x]
F[198,x] = F[199,x]
F[199,x] = F[200,x]*F[4,x]
F[200,x] = F[201,x]+F[202,x]
F[201,x] = F[191,x]
F[202,x] = F[203,x]
F[203,x] = F[204,x]*F[4,x]
F[204,x] = F[205,x]+F[206,x]
F[205,x] = F[191,x]
F[206,x] = F[203,x]
F[207,x] = F[208,x]
F[208,x] = F[209,x]*F[4,x]
F[209,x] = F[210,x]+F[211,x]
F[210,x] = F[182,x]
F[211,x] = F[208,x]
F[212,x] = 3*F[15,x]+F[213,x]+F[235,x]
F[213,x] = F[214,x]*F[4,x]
F[214,x] = F[215,x]+F[220,x]
F[215,x] = F[136,x]+F[216,x]
F[216,x] = F[217,x]
F[217,x] = F[218,x]*F[4,x]
F[218,x] = F[219,x]+F[32,x]
F[219,x] = F[145,x]
F[220,x] = F[221,x]+F[226,x]
F[221,x] = F[222,x]
F[222,x] = F[223,x]*F[4,x]
F[223,x] = F[224,x]+F[225,x]
F[224,x] = F[136,x]
F[225,x] = F[221,x]
F[226,x] = F[227,x]
F[227,x] = F[228,x]*F[4,x]
F[228,x] = F[229,x]+F[230,x]
F[229,x] = F[216,x]
F[230,x] = F[231,x]
F[231,x] = F[232,x]*F[4,x]
F[232,x] = F[233,x]+F[234,x]
F[233,x] = F[216,x]
F[234,x] = F[231,x]
F[235,x] = F[236,x]*F[4,x]
F[236,x] = F[237,x]+F[238,x]
F[237,x] = F[182,x]
F[238,x] = F[208,x]
F[239,x] = F[240,x]*F[4,x]
F[240,x] = F[241,x]+F[267,x]
F[241,x] = F[101,x]+F[242,x]
F[242,x] = F[243,x]
F[243,x] = F[244,x]*F[4,x]
F[244,x] = F[245,x]+F[246,x]
F[245,x] = F[19,x]+F[28,x]
F[246,x] = F[182,x]+F[247,x]
F[247,x] = 3*F[15,x]+F[235,x]+F[248,x]
F[248,x] = F[249,x]*F[4,x]
F[249,x] = F[250,x]+F[252,x]
F[250,x] = F[251,x]+F[28,x]
F[251,x] = F[217,x]
F[252,x] = F[253,x]+F[258,x]
F[253,x] = F[254,x]
F[254,x] = F[255,x]*F[4,x]
F[255,x] = F[256,x]+F[257,x]
F[256,x] = F[28,x]
F[257,x] = F[253,x]
F[258,x] = F[259,x]
F[259,x] = F[260,x]*F[4,x]
F[260,x] = F[261,x]+F[262,x]
F[261,x] = F[251,x]
F[262,x] = F[263,x]
F[263,x] = F[264,x]*F[4,x]
F[264,x] = F[265,x]+F[266,x]
F[265,x] = F[251,x]
F[266,x] = F[263,x]
F[267,x] = F[127,x]+F[268,x]
F[268,x] = F[269,x]
F[269,x] = F[270,x]*F[4,x]
F[270,x] = F[271,x]+F[272,x]
F[271,x] = F[182,x]
F[272,x] = F[208,x]
F[273,x] = F[274,x]*F[4,x]
F[274,x] = F[275,x]+F[336,x]
F[275,x] = F[2,x]+F[276,x]
F[276,x] = F[15,x]+F[277,x]+F[333,x]
F[277,x] = F[278,x]*F[4,x]
F[278,x] = F[279,x]+F[280,x]
F[279,x] = F[11,x]+F[14,x]
F[280,x] = F[101,x]+F[281,x]
F[281,x] = 2*F[15,x]+F[239,x]+F[282,x]
F[282,x] = F[283,x]*F[4,x]
F[283,x] = F[284,x]+F[286,x]
F[284,x] = F[14,x]+F[285,x]
F[285,x] = 2*F[15,x]+F[137,x]+F[29,x]
F[286,x] = F[287,x]+F[313,x]
F[287,x] = F[288,x]
F[288,x] = F[289,x]*F[4,x]
F[289,x] = F[290,x]+F[292,x]
F[290,x] = F[14,x]+F[291,x]
F[291,x] = F[34,x]
F[292,x] = F[287,x]+F[293,x]
F[293,x] = 3*F[15,x]+F[179,x]+F[294,x]
F[294,x] = F[295,x]*F[4,x]
F[295,x] = F[296,x]+F[298,x]
F[296,x] = F[291,x]+F[297,x]
F[297,x] = F[161,x]
F[298,x] = F[299,x]+F[304,x]
F[299,x] = F[300,x]
F[300,x] = F[301,x]*F[4,x]
F[301,x] = F[302,x]+F[303,x]
F[302,x] = F[291,x]
F[303,x] = F[299,x]
F[304,x] = F[305,x]
F[305,x] = F[306,x]*F[4,x]
F[306,x] = F[307,x]+F[308,x]
F[307,x] = F[297,x]
F[308,x] = F[309,x]
F[309,x] = F[310,x]*F[4,x]
F[310,x] = F[311,x]+F[312,x]
F[311,x] = F[297,x]
F[312,x] = F[309,x]
F[313,x] = 3*F[15,x]+F[235,x]+F[314,x]
F[314,x] = F[315,x]*F[4,x]
F[315,x] = F[316,x]+F[318,x]
F[316,x] = F[285,x]+F[317,x]
F[317,x] = F[217,x]
F[318,x] = F[319,x]+F[324,x]
F[319,x] = F[320,x]
F[320,x] = F[321,x]*F[4,x]
F[321,x] = F[322,x]+F[323,x]
F[322,x] = F[285,x]
F[323,x] = F[319,x]
F[324,x] = F[325,x]
F[325,x] = F[326,x]*F[4,x]
F[326,x] = F[327,x]+F[328,x]
F[327,x] = F[317,x]
F[328,x] = F[329,x]
F[329,x] = F[330,x]*F[4,x]
F[330,x] = F[331,x]+F[332,x]
F[331,x] = F[317,x]
F[332,x] = F[329,x]
F[333,x] = F[334,x]*F[4,x]
F[334,x] = F[2,x]+F[335,x]
F[335,x] = F[333,x]
F[336,x] = F[337,x]+F[345,x]
F[337,x] = F[338,x]
F[338,x] = F[339,x]*F[4,x]
F[339,x] = F[334,x]+F[340,x]
F[340,x] = F[337,x]+F[341,x]
F[341,x] = F[342,x]
F[342,x] = F[343,x]*F[4,x]
F[343,x] = F[337,x]+F[344,x]
F[344,x] = F[342,x]
F[345,x] = 2*F[15,x]+F[342,x]+F[346,x]
F[346,x] = F[347,x]*F[4,x]
F[347,x] = F[348,x]+F[349,x]
F[348,x] = F[101,x]
F[349,x] = F[127,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_{41}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{38}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)
F_{18}\! \left(x \right) = F_{11}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right)+F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{28}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \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_{27}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right)
F_{27}\! \left(x \right) = F_{23}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{19}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{19}\! \left(x \right)
F_{37}\! \left(x \right) = F_{33}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{7}\! \left(x \right)
F_{40}\! \left(x \right) = F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = F_{2}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{15}\! \left(x \right)+F_{273}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{68}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{7}\! \left(x \right)
F_{46}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{13}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{58}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{39}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{50}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{50}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{55}\! \left(x \right)
F_{58}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{55}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{23}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{23}\! \left(x \right)
F_{67}\! \left(x \right) = F_{63}\! \left(x \right)
F_{68}\! \left(x \right) = F_{132}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{74}\! \left(x \right)
F_{72}\! \left(x \right) = F_{7}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{24}\! \left(x \right)
F_{74}\! \left(x \right) = F_{69}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{76}\! \left(x \right)+F_{98}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{83}\! \left(x \right)
F_{78}\! \left(x \right) = F_{73}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{27}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{63}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{89}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{88}\! \left(x \right)
F_{87}\! \left(x \right) = F_{73}\! \left(x \right)
F_{88}\! \left(x \right) = F_{84}\! \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_{79}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{97}\! \left(x \right)
F_{96}\! \left(x \right) = F_{79}\! \left(x \right)
F_{97}\! \left(x \right) = F_{94}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{126}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{4}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{105}\! \left(x \right)
F_{104}\! \left(x \right) = F_{11}\! \left(x \right)+F_{23}\! \left(x \right)
F_{105}\! \left(x \right) = F_{101}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{107}\! \left(x \right)+F_{98}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{111}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{23}\! \left(x \right)
F_{110}\! \left(x \right) = F_{80}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{117}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{4}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{116}\! \left(x \right)
F_{115}\! \left(x \right) = F_{23}\! \left(x \right)
F_{116}\! \left(x \right) = F_{112}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{121}\! \left(x \right)
F_{120}\! \left(x \right) = F_{110}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{4}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{125}\! \left(x \right)
F_{124}\! \left(x \right) = F_{110}\! \left(x \right)
F_{125}\! \left(x \right) = F_{122}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{4}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{131}\! \left(x \right)
F_{130}\! \left(x \right) = F_{101}\! \left(x \right)
F_{131}\! \left(x \right) = F_{127}\! \left(x \right)
F_{132}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{133}\! \left(x \right)+F_{239}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{4}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{149}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{46}\! \left(x \right)
F_{136}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{137}\! \left(x \right)+F_{29}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{4}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{22}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{63}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{4}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{144}\! \left(x \right)
F_{143}\! \left(x \right) = F_{33}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right) F_{4}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{148}\! \left(x \right)
F_{147}\! \left(x \right) = F_{33}\! \left(x \right)
F_{148}\! \left(x \right) = F_{145}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{212}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{4}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{155}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{46}\! \left(x \right)
F_{154}\! \left(x \right) = F_{34}\! \left(x \right)
F_{155}\! \left(x \right) = F_{150}\! \left(x \right)+F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{157}\! \left(x \right)+F_{179}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right) F_{4}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{164}\! \left(x \right)
F_{159}\! \left(x \right) = F_{154}\! \left(x \right)+F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right) F_{4}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{37}\! \left(x \right)
F_{163}\! \left(x \right) = F_{145}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)+F_{170}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right) F_{4}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)+F_{169}\! \left(x \right)
F_{168}\! \left(x \right) = F_{154}\! \left(x \right)
F_{169}\! \left(x \right) = F_{165}\! \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_{160}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \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_{178}\! \left(x \right)
F_{177}\! \left(x \right) = F_{160}\! \left(x \right)
F_{178}\! \left(x \right) = F_{175}\! \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_{207}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right) F_{4}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{186}\! \left(x \right)
F_{185}\! \left(x \right) = F_{19}\! \left(x \right)+F_{33}\! \left(x \right)
F_{186}\! \left(x \right) = F_{182}\! \left(x \right)+F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{179}\! \left(x \right)+F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right) F_{4}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)+F_{192}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{33}\! \left(x \right)
F_{191}\! \left(x \right) = F_{161}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{198}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right) F_{4}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right)+F_{197}\! \left(x \right)
F_{196}\! \left(x \right) = F_{33}\! \left(x \right)
F_{197}\! \left(x \right) = F_{193}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right) F_{4}\! \left(x \right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right)+F_{202}\! \left(x \right)
F_{201}\! \left(x \right) = F_{191}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right) F_{4}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right)+F_{206}\! \left(x \right)
F_{205}\! \left(x \right) = F_{191}\! \left(x \right)
F_{206}\! \left(x \right) = F_{203}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right) F_{4}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)+F_{211}\! \left(x \right)
F_{210}\! \left(x \right) = F_{182}\! \left(x \right)
F_{211}\! \left(x \right) = F_{208}\! \left(x \right)
F_{212}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{213}\! \left(x \right)+F_{235}\! \left(x \right)
F_{213}\! \left(x \right) = F_{214}\! \left(x \right) F_{4}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right)+F_{220}\! \left(x \right)
F_{215}\! \left(x \right) = F_{136}\! \left(x \right)+F_{216}\! \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_{32}\! \left(x \right)
F_{219}\! \left(x \right) = F_{145}\! \left(x \right)
F_{220}\! \left(x \right) = F_{221}\! \left(x \right)+F_{226}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right) F_{4}\! \left(x \right)
F_{223}\! \left(x \right) = F_{224}\! \left(x \right)+F_{225}\! \left(x \right)
F_{224}\! \left(x \right) = F_{136}\! \left(x \right)
F_{225}\! \left(x \right) = F_{221}\! \left(x \right)
F_{226}\! \left(x \right) = F_{227}\! \left(x \right)
F_{227}\! \left(x \right) = F_{228}\! \left(x \right) F_{4}\! \left(x \right)
F_{228}\! \left(x \right) = F_{229}\! \left(x \right)+F_{230}\! \left(x \right)
F_{229}\! \left(x \right) = F_{216}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right) F_{4}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right)+F_{234}\! \left(x \right)
F_{233}\! \left(x \right) = F_{216}\! \left(x \right)
F_{234}\! \left(x \right) = F_{231}\! \left(x \right)
F_{235}\! \left(x \right) = F_{236}\! \left(x \right) F_{4}\! \left(x \right)
F_{236}\! \left(x \right) = F_{237}\! \left(x \right)+F_{238}\! \left(x \right)
F_{237}\! \left(x \right) = F_{182}\! \left(x \right)
F_{238}\! \left(x \right) = F_{208}\! \left(x \right)
F_{239}\! \left(x \right) = F_{240}\! \left(x \right) F_{4}\! \left(x \right)
F_{240}\! \left(x \right) = F_{241}\! \left(x \right)+F_{267}\! \left(x \right)
F_{241}\! \left(x \right) = F_{101}\! \left(x \right)+F_{242}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x \right)
F_{243}\! \left(x \right) = F_{244}\! \left(x \right) F_{4}\! \left(x \right)
F_{244}\! \left(x \right) = F_{245}\! \left(x \right)+F_{246}\! \left(x \right)
F_{245}\! \left(x \right) = F_{19}\! \left(x \right)+F_{28}\! \left(x \right)
F_{246}\! \left(x \right) = F_{182}\! \left(x \right)+F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{235}\! \left(x \right)+F_{248}\! \left(x \right)
F_{248}\! \left(x \right) = F_{249}\! \left(x \right) F_{4}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right)+F_{252}\! \left(x \right)
F_{250}\! \left(x \right) = F_{251}\! \left(x \right)+F_{28}\! \left(x \right)
F_{251}\! \left(x \right) = F_{217}\! \left(x \right)
F_{252}\! \left(x \right) = F_{253}\! \left(x \right)+F_{258}\! \left(x \right)
F_{253}\! \left(x \right) = F_{254}\! \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_{28}\! \left(x \right)
F_{257}\! \left(x \right) = F_{253}\! \left(x \right)
F_{258}\! \left(x \right) = F_{259}\! \left(x \right)
F_{259}\! \left(x \right) = F_{260}\! \left(x \right) F_{4}\! \left(x \right)
F_{260}\! \left(x \right) = F_{261}\! \left(x \right)+F_{262}\! \left(x \right)
F_{261}\! \left(x \right) = F_{251}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \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_{266}\! \left(x \right)
F_{265}\! \left(x \right) = F_{251}\! \left(x \right)
F_{266}\! \left(x \right) = F_{263}\! \left(x \right)
F_{267}\! \left(x \right) = F_{127}\! \left(x \right)+F_{268}\! \left(x \right)
F_{268}\! \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_{272}\! \left(x \right)
F_{271}\! \left(x \right) = F_{182}\! \left(x \right)
F_{272}\! \left(x \right) = F_{208}\! \left(x \right)
F_{273}\! \left(x \right) = F_{274}\! \left(x \right) F_{4}\! \left(x \right)
F_{274}\! \left(x \right) = F_{275}\! \left(x \right)+F_{336}\! \left(x \right)
F_{275}\! \left(x \right) = F_{2}\! \left(x \right)+F_{276}\! \left(x \right)
F_{276}\! \left(x \right) = F_{15}\! \left(x \right)+F_{277}\! \left(x \right)+F_{333}\! \left(x \right)
F_{277}\! \left(x \right) = F_{278}\! \left(x \right) F_{4}\! \left(x \right)
F_{278}\! \left(x \right) = F_{279}\! \left(x \right)+F_{280}\! \left(x \right)
F_{279}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{280}\! \left(x \right) = F_{101}\! \left(x \right)+F_{281}\! \left(x \right)
F_{281}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{239}\! \left(x \right)+F_{282}\! \left(x \right)
F_{282}\! \left(x \right) = F_{283}\! \left(x \right) F_{4}\! \left(x \right)
F_{283}\! \left(x \right) = F_{284}\! \left(x \right)+F_{286}\! \left(x \right)
F_{284}\! \left(x \right) = F_{14}\! \left(x \right)+F_{285}\! \left(x \right)
F_{285}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{137}\! \left(x \right)+F_{29}\! \left(x \right)
F_{286}\! \left(x \right) = F_{287}\! \left(x \right)+F_{313}\! \left(x \right)
F_{287}\! \left(x \right) = F_{288}\! \left(x \right)
F_{288}\! \left(x \right) = F_{289}\! \left(x \right) F_{4}\! \left(x \right)
F_{289}\! \left(x \right) = F_{290}\! \left(x \right)+F_{292}\! \left(x \right)
F_{290}\! \left(x \right) = F_{14}\! \left(x \right)+F_{291}\! \left(x \right)
F_{291}\! \left(x \right) = F_{34}\! \left(x \right)
F_{292}\! \left(x \right) = F_{287}\! \left(x \right)+F_{293}\! \left(x \right)
F_{293}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{179}\! \left(x \right)+F_{294}\! \left(x \right)
F_{294}\! \left(x \right) = F_{295}\! \left(x \right) F_{4}\! \left(x \right)
F_{295}\! \left(x \right) = F_{296}\! \left(x \right)+F_{298}\! \left(x \right)
F_{296}\! \left(x \right) = F_{291}\! \left(x \right)+F_{297}\! \left(x \right)
F_{297}\! \left(x \right) = F_{161}\! \left(x \right)
F_{298}\! \left(x \right) = F_{299}\! \left(x \right)+F_{304}\! \left(x \right)
F_{299}\! \left(x \right) = F_{300}\! \left(x \right)
F_{300}\! \left(x \right) = F_{301}\! \left(x \right) F_{4}\! \left(x \right)
F_{301}\! \left(x \right) = F_{302}\! \left(x \right)+F_{303}\! \left(x \right)
F_{302}\! \left(x \right) = F_{291}\! \left(x \right)
F_{303}\! \left(x \right) = F_{299}\! \left(x \right)
F_{304}\! \left(x \right) = F_{305}\! \left(x \right)
F_{305}\! \left(x \right) = F_{306}\! \left(x \right) F_{4}\! \left(x \right)
F_{306}\! \left(x \right) = F_{307}\! \left(x \right)+F_{308}\! \left(x \right)
F_{307}\! \left(x \right) = F_{297}\! \left(x \right)
F_{308}\! \left(x \right) = F_{309}\! \left(x \right)
F_{309}\! \left(x \right) = F_{310}\! \left(x \right) F_{4}\! \left(x \right)
F_{310}\! \left(x \right) = F_{311}\! \left(x \right)+F_{312}\! \left(x \right)
F_{311}\! \left(x \right) = F_{297}\! \left(x \right)
F_{312}\! \left(x \right) = F_{309}\! \left(x \right)
F_{313}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{235}\! \left(x \right)+F_{314}\! \left(x \right)
F_{314}\! \left(x \right) = F_{315}\! \left(x \right) F_{4}\! \left(x \right)
F_{315}\! \left(x \right) = F_{316}\! \left(x \right)+F_{318}\! \left(x \right)
F_{316}\! \left(x \right) = F_{285}\! \left(x \right)+F_{317}\! \left(x \right)
F_{317}\! \left(x \right) = F_{217}\! \left(x \right)
F_{318}\! \left(x \right) = F_{319}\! \left(x \right)+F_{324}\! \left(x \right)
F_{319}\! \left(x \right) = F_{320}\! \left(x \right)
F_{320}\! \left(x \right) = F_{321}\! \left(x \right) F_{4}\! \left(x \right)
F_{321}\! \left(x \right) = F_{322}\! \left(x \right)+F_{323}\! \left(x \right)
F_{322}\! \left(x \right) = F_{285}\! \left(x \right)
F_{323}\! \left(x \right) = F_{319}\! \left(x \right)
F_{324}\! \left(x \right) = F_{325}\! \left(x \right)
F_{325}\! \left(x \right) = F_{326}\! \left(x \right) F_{4}\! \left(x \right)
F_{326}\! \left(x \right) = F_{327}\! \left(x \right)+F_{328}\! \left(x \right)
F_{327}\! \left(x \right) = F_{317}\! \left(x \right)
F_{328}\! \left(x \right) = F_{329}\! \left(x \right)
F_{329}\! \left(x \right) = F_{330}\! \left(x \right) F_{4}\! \left(x \right)
F_{330}\! \left(x \right) = F_{331}\! \left(x \right)+F_{332}\! \left(x \right)
F_{331}\! \left(x \right) = F_{317}\! \left(x \right)
F_{332}\! \left(x \right) = F_{329}\! \left(x \right)
F_{333}\! \left(x \right) = F_{334}\! \left(x \right) F_{4}\! \left(x \right)
F_{334}\! \left(x \right) = F_{2}\! \left(x \right)+F_{335}\! \left(x \right)
F_{335}\! \left(x \right) = F_{333}\! \left(x \right)
F_{336}\! \left(x \right) = F_{337}\! \left(x \right)+F_{345}\! \left(x \right)
F_{337}\! \left(x \right) = F_{338}\! \left(x \right)
F_{338}\! \left(x \right) = F_{339}\! \left(x \right) F_{4}\! \left(x \right)
F_{339}\! \left(x \right) = F_{334}\! \left(x \right)+F_{340}\! \left(x \right)
F_{340}\! \left(x \right) = F_{337}\! \left(x \right)+F_{341}\! \left(x \right)
F_{341}\! \left(x \right) = F_{342}\! \left(x \right)
F_{342}\! \left(x \right) = F_{343}\! \left(x \right) F_{4}\! \left(x \right)
F_{343}\! \left(x \right) = F_{337}\! \left(x \right)+F_{344}\! \left(x \right)
F_{344}\! \left(x \right) = F_{342}\! \left(x \right)
F_{345}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{342}\! \left(x \right)+F_{346}\! \left(x \right)
F_{346}\! \left(x \right) = F_{347}\! \left(x \right) F_{4}\! \left(x \right)
F_{347}\! \left(x \right) = F_{348}\! \left(x \right)+F_{349}\! \left(x \right)
F_{348}\! \left(x \right) = F_{101}\! \left(x \right)
F_{349}\! \left(x \right) = F_{127}\! \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_41(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_7(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_38(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_22(x))
Eq(F_18(x), F_11(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_11(x) + F_19(x))
Eq(F_22(x), F_23(x) + F_28(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_26(x) + F_27(x))
Eq(F_26(x), F_11(x))
Eq(F_27(x), F_23(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_19(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_19(x))
Eq(F_37(x), F_33(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_7(x))
Eq(F_40(x), F_38(x))
Eq(F_41(x), F_2(x) + F_42(x))
Eq(F_42(x), F_15(x) + F_273(x) + F_43(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_68(x))
Eq(F_45(x), F_46(x) + F_7(x))
Eq(F_46(x), F_15(x) + F_16(x) + F_47(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_13(x) + F_49(x))
Eq(F_49(x), F_50(x) + F_58(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_39(x) + F_53(x))
Eq(F_53(x), F_50(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_50(x) + F_57(x))
Eq(F_57(x), F_55(x))
Eq(F_58(x), 2*F_15(x) + F_55(x) + F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_23(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_23(x))
Eq(F_67(x), F_63(x))
Eq(F_68(x), F_132(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_74(x))
Eq(F_72(x), F_7(x) + F_73(x))
Eq(F_73(x), F_24(x))
Eq(F_74(x), F_69(x) + F_75(x))
Eq(F_75(x), 2*F_15(x) + F_76(x) + F_98(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_83(x))
Eq(F_78(x), F_73(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_4(x)*F_81(x))
Eq(F_81(x), F_27(x) + F_82(x))
Eq(F_82(x), F_63(x))
Eq(F_83(x), F_84(x) + F_89(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_87(x) + F_88(x))
Eq(F_87(x), F_73(x))
Eq(F_88(x), F_84(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_79(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_4(x)*F_95(x))
Eq(F_95(x), F_96(x) + F_97(x))
Eq(F_96(x), F_79(x))
Eq(F_97(x), F_94(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_126(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_4(x))
Eq(F_103(x), F_104(x) + F_105(x))
Eq(F_104(x), F_11(x) + F_23(x))
Eq(F_105(x), F_101(x) + F_106(x))
Eq(F_106(x), F_107(x) + 2*F_15(x) + F_98(x))
Eq(F_107(x), F_108(x)*F_4(x))
Eq(F_108(x), F_109(x) + F_111(x))
Eq(F_109(x), F_110(x) + F_23(x))
Eq(F_110(x), F_80(x))
Eq(F_111(x), F_112(x) + F_117(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x)*F_4(x))
Eq(F_114(x), F_115(x) + F_116(x))
Eq(F_115(x), F_23(x))
Eq(F_116(x), F_112(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_119(x)*F_4(x))
Eq(F_119(x), F_120(x) + F_121(x))
Eq(F_120(x), F_110(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x)*F_4(x))
Eq(F_123(x), F_124(x) + F_125(x))
Eq(F_124(x), F_110(x))
Eq(F_125(x), F_122(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_129(x)*F_4(x))
Eq(F_129(x), F_130(x) + F_131(x))
Eq(F_130(x), F_101(x))
Eq(F_131(x), F_127(x))
Eq(F_132(x), F_133(x) + 2*F_15(x) + F_239(x))
Eq(F_133(x), F_134(x)*F_4(x))
Eq(F_134(x), F_135(x) + F_149(x))
Eq(F_135(x), F_136(x) + F_46(x))
Eq(F_136(x), F_137(x) + 2*F_15(x) + F_29(x))
Eq(F_137(x), F_138(x)*F_4(x))
Eq(F_138(x), F_139(x) + F_22(x))
Eq(F_139(x), F_140(x) + F_63(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_142(x)*F_4(x))
Eq(F_142(x), F_143(x) + F_144(x))
Eq(F_143(x), F_33(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_146(x)*F_4(x))
Eq(F_146(x), F_147(x) + F_148(x))
Eq(F_147(x), F_33(x))
Eq(F_148(x), F_145(x))
Eq(F_149(x), F_150(x) + F_212(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_152(x)*F_4(x))
Eq(F_152(x), F_153(x) + F_155(x))
Eq(F_153(x), F_154(x) + F_46(x))
Eq(F_154(x), F_34(x))
Eq(F_155(x), F_150(x) + F_156(x))
Eq(F_156(x), 3*F_15(x) + F_157(x) + F_179(x))
Eq(F_157(x), F_158(x)*F_4(x))
Eq(F_158(x), F_159(x) + F_164(x))
Eq(F_159(x), F_154(x) + F_160(x))
Eq(F_160(x), F_161(x))
Eq(F_161(x), F_162(x)*F_4(x))
Eq(F_162(x), F_163(x) + F_37(x))
Eq(F_163(x), F_145(x))
Eq(F_164(x), F_165(x) + F_170(x))
Eq(F_165(x), F_166(x))
Eq(F_166(x), F_167(x)*F_4(x))
Eq(F_167(x), F_168(x) + F_169(x))
Eq(F_168(x), F_154(x))
Eq(F_169(x), F_165(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_160(x))
Eq(F_174(x), F_175(x))
Eq(F_175(x), F_176(x)*F_4(x))
Eq(F_176(x), F_177(x) + F_178(x))
Eq(F_177(x), F_160(x))
Eq(F_178(x), F_175(x))
Eq(F_179(x), F_180(x)*F_4(x))
Eq(F_180(x), F_181(x) + F_207(x))
Eq(F_181(x), F_182(x))
Eq(F_182(x), F_183(x))
Eq(F_183(x), F_184(x)*F_4(x))
Eq(F_184(x), F_185(x) + F_186(x))
Eq(F_185(x), F_19(x) + F_33(x))
Eq(F_186(x), F_182(x) + F_187(x))
Eq(F_187(x), 3*F_15(x) + F_179(x) + F_188(x))
Eq(F_188(x), F_189(x)*F_4(x))
Eq(F_189(x), F_190(x) + F_192(x))
Eq(F_190(x), F_191(x) + F_33(x))
Eq(F_191(x), F_161(x))
Eq(F_192(x), F_193(x) + F_198(x))
Eq(F_193(x), F_194(x))
Eq(F_194(x), F_195(x)*F_4(x))
Eq(F_195(x), F_196(x) + F_197(x))
Eq(F_196(x), F_33(x))
Eq(F_197(x), F_193(x))
Eq(F_198(x), F_199(x))
Eq(F_199(x), F_200(x)*F_4(x))
Eq(F_200(x), F_201(x) + F_202(x))
Eq(F_201(x), F_191(x))
Eq(F_202(x), F_203(x))
Eq(F_203(x), F_204(x)*F_4(x))
Eq(F_204(x), F_205(x) + F_206(x))
Eq(F_205(x), F_191(x))
Eq(F_206(x), F_203(x))
Eq(F_207(x), F_208(x))
Eq(F_208(x), F_209(x)*F_4(x))
Eq(F_209(x), F_210(x) + F_211(x))
Eq(F_210(x), F_182(x))
Eq(F_211(x), F_208(x))
Eq(F_212(x), 3*F_15(x) + F_213(x) + F_235(x))
Eq(F_213(x), F_214(x)*F_4(x))
Eq(F_214(x), F_215(x) + F_220(x))
Eq(F_215(x), F_136(x) + F_216(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_32(x))
Eq(F_219(x), F_145(x))
Eq(F_220(x), F_221(x) + F_226(x))
Eq(F_221(x), F_222(x))
Eq(F_222(x), F_223(x)*F_4(x))
Eq(F_223(x), F_224(x) + F_225(x))
Eq(F_224(x), F_136(x))
Eq(F_225(x), F_221(x))
Eq(F_226(x), F_227(x))
Eq(F_227(x), F_228(x)*F_4(x))
Eq(F_228(x), F_229(x) + F_230(x))
Eq(F_229(x), F_216(x))
Eq(F_230(x), F_231(x))
Eq(F_231(x), F_232(x)*F_4(x))
Eq(F_232(x), F_233(x) + F_234(x))
Eq(F_233(x), F_216(x))
Eq(F_234(x), F_231(x))
Eq(F_235(x), F_236(x)*F_4(x))
Eq(F_236(x), F_237(x) + F_238(x))
Eq(F_237(x), F_182(x))
Eq(F_238(x), F_208(x))
Eq(F_239(x), F_240(x)*F_4(x))
Eq(F_240(x), F_241(x) + F_267(x))
Eq(F_241(x), F_101(x) + F_242(x))
Eq(F_242(x), F_243(x))
Eq(F_243(x), F_244(x)*F_4(x))
Eq(F_244(x), F_245(x) + F_246(x))
Eq(F_245(x), F_19(x) + F_28(x))
Eq(F_246(x), F_182(x) + F_247(x))
Eq(F_247(x), 3*F_15(x) + F_235(x) + F_248(x))
Eq(F_248(x), F_249(x)*F_4(x))
Eq(F_249(x), F_250(x) + F_252(x))
Eq(F_250(x), F_251(x) + F_28(x))
Eq(F_251(x), F_217(x))
Eq(F_252(x), F_253(x) + F_258(x))
Eq(F_253(x), F_254(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_28(x))
Eq(F_257(x), F_253(x))
Eq(F_258(x), F_259(x))
Eq(F_259(x), F_260(x)*F_4(x))
Eq(F_260(x), F_261(x) + F_262(x))
Eq(F_261(x), F_251(x))
Eq(F_262(x), F_263(x))
Eq(F_263(x), F_264(x)*F_4(x))
Eq(F_264(x), F_265(x) + F_266(x))
Eq(F_265(x), F_251(x))
Eq(F_266(x), F_263(x))
Eq(F_267(x), F_127(x) + F_268(x))
Eq(F_268(x), F_269(x))
Eq(F_269(x), F_270(x)*F_4(x))
Eq(F_270(x), F_271(x) + F_272(x))
Eq(F_271(x), F_182(x))
Eq(F_272(x), F_208(x))
Eq(F_273(x), F_274(x)*F_4(x))
Eq(F_274(x), F_275(x) + F_336(x))
Eq(F_275(x), F_2(x) + F_276(x))
Eq(F_276(x), F_15(x) + F_277(x) + F_333(x))
Eq(F_277(x), F_278(x)*F_4(x))
Eq(F_278(x), F_279(x) + F_280(x))
Eq(F_279(x), F_11(x) + F_14(x))
Eq(F_280(x), F_101(x) + F_281(x))
Eq(F_281(x), 2*F_15(x) + F_239(x) + F_282(x))
Eq(F_282(x), F_283(x)*F_4(x))
Eq(F_283(x), F_284(x) + F_286(x))
Eq(F_284(x), F_14(x) + F_285(x))
Eq(F_285(x), F_137(x) + 2*F_15(x) + F_29(x))
Eq(F_286(x), F_287(x) + F_313(x))
Eq(F_287(x), F_288(x))
Eq(F_288(x), F_289(x)*F_4(x))
Eq(F_289(x), F_290(x) + F_292(x))
Eq(F_290(x), F_14(x) + F_291(x))
Eq(F_291(x), F_34(x))
Eq(F_292(x), F_287(x) + F_293(x))
Eq(F_293(x), 3*F_15(x) + F_179(x) + F_294(x))
Eq(F_294(x), F_295(x)*F_4(x))
Eq(F_295(x), F_296(x) + F_298(x))
Eq(F_296(x), F_291(x) + F_297(x))
Eq(F_297(x), F_161(x))
Eq(F_298(x), F_299(x) + F_304(x))
Eq(F_299(x), F_300(x))
Eq(F_300(x), F_301(x)*F_4(x))
Eq(F_301(x), F_302(x) + F_303(x))
Eq(F_302(x), F_291(x))
Eq(F_303(x), F_299(x))
Eq(F_304(x), F_305(x))
Eq(F_305(x), F_306(x)*F_4(x))
Eq(F_306(x), F_307(x) + F_308(x))
Eq(F_307(x), F_297(x))
Eq(F_308(x), F_309(x))
Eq(F_309(x), F_310(x)*F_4(x))
Eq(F_310(x), F_311(x) + F_312(x))
Eq(F_311(x), F_297(x))
Eq(F_312(x), F_309(x))
Eq(F_313(x), 3*F_15(x) + F_235(x) + F_314(x))
Eq(F_314(x), F_315(x)*F_4(x))
Eq(F_315(x), F_316(x) + F_318(x))
Eq(F_316(x), F_285(x) + F_317(x))
Eq(F_317(x), F_217(x))
Eq(F_318(x), F_319(x) + F_324(x))
Eq(F_319(x), F_320(x))
Eq(F_320(x), F_321(x)*F_4(x))
Eq(F_321(x), F_322(x) + F_323(x))
Eq(F_322(x), F_285(x))
Eq(F_323(x), F_319(x))
Eq(F_324(x), F_325(x))
Eq(F_325(x), F_326(x)*F_4(x))
Eq(F_326(x), F_327(x) + F_328(x))
Eq(F_327(x), F_317(x))
Eq(F_328(x), F_329(x))
Eq(F_329(x), F_330(x)*F_4(x))
Eq(F_330(x), F_331(x) + F_332(x))
Eq(F_331(x), F_317(x))
Eq(F_332(x), F_329(x))
Eq(F_333(x), F_334(x)*F_4(x))
Eq(F_334(x), F_2(x) + F_335(x))
Eq(F_335(x), F_333(x))
Eq(F_336(x), F_337(x) + F_345(x))
Eq(F_337(x), F_338(x))
Eq(F_338(x), F_339(x)*F_4(x))
Eq(F_339(x), F_334(x) + F_340(x))
Eq(F_340(x), F_337(x) + F_341(x))
Eq(F_341(x), F_342(x))
Eq(F_342(x), F_343(x)*F_4(x))
Eq(F_343(x), F_337(x) + F_344(x))
Eq(F_344(x), F_342(x))
Eq(F_345(x), 2*F_15(x) + F_342(x) + F_346(x))
Eq(F_346(x), F_347(x)*F_4(x))
Eq(F_347(x), F_348(x) + F_349(x))
Eq(F_348(x), F_101(x))
Eq(F_349(x), F_127(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 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": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 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": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 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