0213_1320_2301

Counting sequence:
1, 1, 2, 6, 21, 73, 239, 740, 2194, 6298, 17653, 48621, 132199, 356040, 952154, 2533014, 6712221, 17734489, 46753127, 123048884, 323441770, 849373210, 2228871757, 5845630221, 15324795631, 40162310568, 105229244354, 275659639590, 722018109189, 1890931558153, 4951850306303, 12966766843556, 33952745190754, 88900058662330, 232764610664389, 609428133068109, 1595588508015511, 4177474829930664, 10937110859682122, 28634407504928214, 74967211166728845, 196269425018512345, 513845461935317687, 1345275756880461236, 3521999400892108666, 9220757630167951738, 24140343858355922269, 63200414682388168365, 165461181663785291359, 433183693258921124808, 1134091024012884923378, 2969091630579547328166, 7773188371325384429109, 20350482490595860697545, 53278277114860707142799, 139484384882783279692004, 365174949591083169858226, 956040608005654305735514, 2502947162656255899056917, 6552801456423865694855469, 17155458359536845792353095, 44913575928029680895894280, 117585274036238215322714042, 307842255404057001927019926, 805941510622676864167893501, 2109982313357461737995759833, 5524005503236684644657588359, 14462034343926544785653413940, 37862097823690854891655474954, 99124259717441830248018658138, 259510682509226256569811798253, 679407790171420180896239338701, 1778712692727400768988551426639, 4656730297455515091808705363560, 12191478218528610437916145513634, 31917704395909248084896892881574, 83561635044756997542688856544741, 218767200889477471994998323585289, 572739967925906873345963407881887, 1499452703492706057850206487407524, 3925618143761137119819285229040770, 10277401730208556940836907549120890, 26906587051700236981149954117140197, 70442359434563560559529988199942541, 184420491271333257811274077277979511, 482819114418121839101960377224586728, 1264036852060403511949943321576968874, 3309291441917831201658542121868703190, 8663837474002575102847028112753914349, 22682220980708864126525232353842594393, 59382825469361957316014049223672985303, 155466255429852887900087675866974602036, 407015940825148466541390499476847309594, 1065581567055496032038366864762760312250, 2789728760361146670202276179209819606269, 7303604714067558059825593841663470473069, 19121085381920755671788769683374135754431, 50059651431853165280569243883646024681864, 131057868913955652819976019317938114083282, 343113955310647618479472928770916669161254, 898283997019254853218670996396308596596245

Generating function in Maple syntax:
(2*x^7-x^6-4*x^5+16*x^4-24*x^3+19*x^2-7*x+1)/(2*x-1)/(x^2-3*x+1)/(x-1)^3

Generating function in latex syntax:
\frac{2 x^{7}-x^{6}-4 x^{5}+16 x^{4}-24 x^{3}+19 x^{2}-7 x +1}{\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x -1\right)^{3}}

Generating function in sympy syntax:
(2*x**7 - x**6 - 4*x**5 + 16*x**4 - 24*x**3 + 19*x**2 - 7*x + 1)/((x - 1)**3*(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)^3*F(x)+2*x^7-x^6-4*x^5+16*x^4-24*x^3+19*x^2-7*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)^{3} F \! \left(x \right)+2 x^{7}-x^{6}-4 x^{5}+16 x^{4}-24 x^{3}+19 x^{2}-7 x +1 = 0

Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/10*(31*5^(1/2)-55)*(3/2-1/2*5^(1/2))^(-n)+1/10*(-31*5^(1/2)-55)*(3/2+1/2*5^(1/2))^(-n)+n^2-2*n-4*2^n+10)

Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{\left(31 \sqrt{5}-55\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{10}+\frac{\left(-31 \sqrt{5}-55\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{10}+n^{2}-2 n -\\4 \,2^{n}+10 & \mathit{\text{otherwise}} \end{array}\right.

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 73
a(6) = 239
a(7) = 740
a(n+3) = n^2+2*a(n)-7*a(n+1)+5*a(n+2)-2*n+6, n >= 8

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) = 73
a \! \left(6\right) = 239
a \! \left(7\right) = 740
a \! \left(n +3\right) = n^{2}+2 a \! \left(n \right)-7 a \! \left(n +1\right)+5 a \! \left(n +2\right)-2 n +6, \quad n \geq 8

Specification 1
Strategy pack name: row_placements
Tree: http://permpal.com/tree/337/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[12,x]*F[3,x]
F[3,x] = F[1,x]+F[132,x]+F[4,x]
F[4,x] = F[12,x]*F[5,x]
F[5,x] = F[1,x]+F[17,x]+F[4,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[14,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[8,x]
F[12,x] = x
F[13,x] = F[10,x]*F[14,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[12,x]*F[14,x]
F[17,x] = F[12,x]*F[18,x]
F[18,x] = F[1,x]+F[107,x]+F[113,x]+F[19,x]+F[6,x]
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[1,x]+F[105,x]+F[19,x]+F[21,x]+F[6,x]
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[1,x]+F[103,x]+F[23,x]+F[76,x]
F[23,x] = F[12,x]*F[24,x]
F[24,x] = F[1,x]+F[25,x]+F[27,x]+F[35,x]+F[74,x]
F[25,x] = F[12,x]*F[26,x]
F[26,x] = F[1,x]+F[25,x]+F[27,x]+F[35,x]+F[36,x]+F[6,x]
F[27,x] = F[28,x]
F[28,x] = F[12,x]*F[14,x]*F[29,x]
F[29,x] = F[1,x]+F[30,x]+F[34,x]
F[30,x] = F[31,x]
F[31,x] = F[12,x]*F[32,x]
F[32,x] = F[29,x]+F[33,x]
F[33,x] = F[12,x]*F[14,x]*F[29,x]
F[34,x] = F[12,x]*F[29,x]
F[35,x] = F[12,x]*F[24,x]
F[36,x] = F[37,x]
F[37,x] = F[12,x]*F[14,x]*F[38,x]
F[38,x] = F[39,x]+F[49,x]+F[72,x]+F[9,x]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[33,x]+F[41,x]
F[41,x] = F[1,x]+F[34,x]+F[42,x]+F[44,x]+F[48,x]
F[42,x] = F[43,x]
F[43,x] = F[12,x]*F[40,x]
F[44,x] = F[12,x]*F[45,x]
F[45,x] = F[1,x]+F[34,x]+F[44,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[12,x]*F[38,x]
F[48,x] = F[12,x]*F[41,x]
F[49,x] = F[12,x]*F[50,x]
F[50,x] = F[51,x]+F[59,x]
F[51,x] = F[52,x]+F[55,x]
F[52,x] = F[1,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[12,x]*F[52,x]
F[55,x] = F[53,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[12,x]*F[58,x]
F[58,x] = F[53,x]+F[56,x]
F[59,x] = F[60,x]+F[66,x]
F[60,x] = F[15,x]+F[61,x]
F[61,x] = F[62,x]+F[63,x]+F[65,x]
F[62,x] = 0
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[53,x]+F[61,x]
F[65,x] = F[12,x]*F[60,x]
F[66,x] = F[61,x]+F[67,x]
F[67,x] = 2*F[62,x]+F[68,x]+F[70,x]
F[68,x] = F[12,x]*F[69,x]
F[69,x] = F[56,x]+F[67,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[61,x]+F[67,x]
F[72,x] = F[12,x]*F[73,x]
F[73,x] = F[52,x]+F[60,x]
F[74,x] = F[75,x]
F[75,x] = F[12,x]*F[14,x]*F[45,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[78,x]+F[86,x]
F[78,x] = F[14,x]+F[79,x]
F[79,x] = F[53,x]+F[80,x]
F[80,x] = F[62,x]+F[81,x]+F[83,x]
F[81,x] = F[12,x]*F[82,x]
F[82,x] = F[15,x]+F[80,x]
F[83,x] = F[12,x]*F[84,x]
F[84,x] = F[53,x]+F[85,x]
F[85,x] = F[83,x]
F[86,x] = F[87,x]+F[94,x]
F[87,x] = F[15,x]+F[88,x]
F[88,x] = F[62,x]+F[89,x]+F[91,x]
F[89,x] = F[12,x]*F[90,x]
F[90,x] = F[15,x]+F[88,x]
F[91,x] = F[12,x]*F[92,x]
F[92,x] = F[15,x]+F[93,x]
F[93,x] = F[91,x]
F[94,x] = F[61,x]+F[95,x]
F[95,x] = F[100,x]+F[62,x]+F[96,x]+F[98,x]
F[96,x] = F[12,x]*F[97,x]
F[97,x] = F[80,x]+F[95,x]
F[98,x] = F[12,x]*F[99,x]
F[99,x] = F[88,x]+F[95,x]
F[100,x] = F[101,x]*F[12,x]
F[101,x] = F[102,x]+F[61,x]
F[102,x] = F[100,x]
F[103,x] = F[104,x]
F[104,x] = F[12,x]*F[14,x]*F[73,x]
F[105,x] = F[106,x]
F[106,x] = F[12,x]*F[14,x]*F[32,x]
F[107,x] = F[108,x]*F[12,x]
F[108,x] = F[1,x]+F[107,x]+F[109,x]+F[19,x]+F[6,x]
F[109,x] = F[110,x]
F[110,x] = F[111,x]*F[12,x]*F[14,x]
F[111,x] = F[1,x]+F[112,x]+F[30,x]+F[6,x]
F[112,x] = F[111,x]*F[12,x]
F[113,x] = F[114,x]*F[12,x]
F[114,x] = F[1,x]+F[112,x]+F[115,x]+F[120,x]+F[126,x]+F[6,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[12,x]
F[117,x] = F[118,x]+F[119,x]
F[118,x] = 2*F[34,x]+F[1,x]+F[115,x]
F[119,x] = F[7,x]
F[120,x] = F[12,x]*F[121,x]
F[121,x] = F[1,x]+F[112,x]+F[115,x]+F[120,x]+F[122,x]+F[6,x]
F[122,x] = F[123,x]
F[123,x] = F[12,x]*F[124,x]*F[14,x]
F[124,x] = F[1,x]+F[112,x]+F[115,x]+F[125,x]+F[6,x]
F[125,x] = F[12,x]*F[124,x]
F[126,x] = F[127,x]
F[127,x] = F[12,x]*F[124,x]*F[128,x]
F[128,x] = F[1,x]+F[129,x]+F[130,x]
F[129,x] = F[12,x]*F[78,x]
F[130,x] = F[131,x]
F[131,x] = F[12,x]*F[128,x]*F[52,x]
F[132,x] = F[12,x]*F[133,x]
F[133,x] = F[1,x]+F[134,x]+F[19,x]+F[21,x]
F[134,x] = F[12,x]*F[135,x]
F[135,x] = F[1,x]+F[115,x]+F[136,x]+F[206,x]+F[34,x]
F[136,x] = F[12,x]*F[137,x]
F[137,x] = F[1,x]+F[138,x]+F[149,x]+F[202,x]+F[204,x]
F[138,x] = F[12,x]*F[139,x]
F[139,x] = F[1,x]+F[140,x]+F[144,x]+F[145,x]+F[34,x]+F[44,x]
F[140,x] = F[141,x]
F[141,x] = F[12,x]*F[142,x]
F[142,x] = F[143,x]+F[33,x]
F[143,x] = 2*F[44,x]+F[1,x]+F[140,x]+F[34,x]
F[144,x] = F[12,x]*F[139,x]
F[145,x] = F[146,x]
F[146,x] = F[12,x]*F[14,x]*F[147,x]
F[147,x] = F[1,x]+F[140,x]+F[148,x]+F[34,x]+F[44,x]
F[148,x] = F[12,x]*F[147,x]
F[149,x] = F[12,x]*F[150,x]
F[150,x] = F[151,x]+F[161,x]
F[151,x] = F[152,x]+F[78,x]
F[152,x] = F[153,x]+F[157,x]
F[153,x] = F[154,x]+F[53,x]
F[154,x] = F[155,x]
F[155,x] = F[12,x]*F[156,x]
F[156,x] = F[15,x]+F[154,x]
F[157,x] = F[158,x]+F[56,x]
F[158,x] = F[159,x]
F[159,x] = F[12,x]*F[160,x]
F[160,x] = F[158,x]+F[80,x]
F[161,x] = F[162,x]+F[184,x]
F[162,x] = F[163,x]+F[167,x]
F[163,x] = F[15,x]+F[164,x]
F[164,x] = F[165,x]
F[165,x] = F[12,x]*F[166,x]
F[166,x] = F[15,x]+F[164,x]
F[167,x] = F[168,x]+F[176,x]
F[168,x] = F[169,x]+F[171,x]+F[62,x]
F[169,x] = F[12,x]*F[170,x]
F[170,x] = F[168,x]+F[53,x]
F[171,x] = F[12,x]*F[172,x]
F[172,x] = F[15,x]+F[173,x]
F[173,x] = F[174,x]
F[174,x] = F[12,x]*F[175,x]
F[175,x] = F[173,x]+F[53,x]
F[176,x] = 2*F[62,x]+F[177,x]+F[179,x]
F[177,x] = F[12,x]*F[178,x]
F[178,x] = F[176,x]+F[80,x]
F[179,x] = F[12,x]*F[180,x]
F[180,x] = F[164,x]+F[181,x]
F[181,x] = F[182,x]
F[182,x] = F[12,x]*F[183,x]
F[183,x] = F[181,x]+F[80,x]
F[184,x] = F[185,x]+F[191,x]
F[185,x] = F[186,x]+F[61,x]
F[186,x] = 2*F[62,x]+F[187,x]+F[189,x]
F[187,x] = F[12,x]*F[188,x]
F[188,x] = F[154,x]+F[186,x]
F[189,x] = F[12,x]*F[190,x]
F[190,x] = F[164,x]+F[186,x]
F[191,x] = F[192,x]+F[197,x]
F[192,x] = 2*F[62,x]+F[193,x]+F[195,x]
F[193,x] = F[12,x]*F[194,x]
F[194,x] = F[192,x]+F[56,x]
F[195,x] = F[12,x]*F[196,x]
F[196,x] = F[168,x]+F[192,x]
F[197,x] = 3*F[62,x]+F[198,x]+F[200,x]
F[198,x] = F[12,x]*F[199,x]
F[199,x] = F[158,x]+F[197,x]
F[200,x] = F[12,x]*F[201,x]
F[201,x] = F[176,x]+F[197,x]
F[202,x] = F[203,x]
F[203,x] = F[12,x]*F[14,x]*F[78,x]
F[204,x] = F[205,x]
F[205,x] = F[12,x]*F[14,x]*F[52,x]
F[206,x] = F[207,x]
F[207,x] = F[12,x]*F[128,x]*F[208,x]
F[208,x] = F[1,x]+F[209,x]+F[210,x]+F[215,x]
F[209,x] = F[12,x]*F[147,x]
F[210,x] = F[12,x]*F[211,x]
F[211,x] = F[212,x]+F[51,x]
F[212,x] = F[213,x]+F[214,x]
F[213,x] = F[15,x]+F[168,x]
F[214,x] = F[192,x]+F[61,x]
F[215,x] = F[216,x]
F[216,x] = F[12,x]*F[14,x]*F[52,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_{12}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{132}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{12}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)+F_{4}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{10}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{17}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{107}\! \left(x \right)+F_{113}\! \left(x \right)+F_{19}\! \left(x \right)+F_{6}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{105}\! \left(x \right)+F_{19}\! \left(x \right)+F_{21}\! \left(x \right)+F_{6}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{103}\! \left(x \right)+F_{23}\! \left(x \right)+F_{76}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)+F_{27}\! \left(x \right)+F_{35}\! \left(x \right)+F_{74}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)+F_{27}\! \left(x \right)+F_{35}\! \left(x \right)+F_{36}\! \left(x \right)+F_{6}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)+F_{34}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{29}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{29}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{49}\! \left(x \right)+F_{72}\! \left(x \right)+F_{9}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{33}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{1}\! \left(x \right)+F_{34}\! \left(x \right)+F_{42}\! \left(x \right)+F_{44}\! \left(x \right)+F_{48}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{1}\! \left(x \right)+F_{34}\! \left(x \right)+F_{44}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{59}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{55}\! \left(x \right)
F_{52}\! \left(x \right) = F_{1}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{53}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{53}\! \left(x \right)+F_{56}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{66}\! \left(x \right)
F_{60}\! \left(x \right) = F_{15}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{63}\! \left(x \right)+F_{65}\! \left(x \right)
F_{62}\! \left(x \right) = 0
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{53}\! \left(x \right)+F_{61}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{66}\! \left(x \right) = F_{61}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = 2 F_{62}\! \left(x \right)+F_{68}\! \left(x \right)+F_{70}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{56}\! \left(x \right)+F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{61}\! \left(x \right)+F_{67}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{52}\! \left(x \right)+F_{60}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{45}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{86}\! \left(x \right)
F_{78}\! \left(x \right) = F_{14}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{53}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{62}\! \left(x \right)+F_{81}\! \left(x \right)+F_{83}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{15}\! \left(x \right)+F_{80}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{53}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{94}\! \left(x \right)
F_{87}\! \left(x \right) = F_{15}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{62}\! \left(x \right)+F_{89}\! \left(x \right)+F_{91}\! \left(x \right)
F_{89}\! \left(x \right) = F_{12}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{15}\! \left(x \right)+F_{88}\! \left(x \right)
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{15}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{91}\! \left(x \right)
F_{94}\! \left(x \right) = F_{61}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{100}\! \left(x \right)+F_{62}\! \left(x \right)+F_{96}\! \left(x \right)+F_{98}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{80}\! \left(x \right)+F_{95}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{88}\! \left(x \right)+F_{95}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{12}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{61}\! \left(x \right)
F_{102}\! \left(x \right) = F_{100}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{73}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{32}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{12}\! \left(x \right)
F_{108}\! \left(x \right) = F_{1}\! \left(x \right)+F_{107}\! \left(x \right)+F_{109}\! \left(x \right)+F_{19}\! \left(x \right)+F_{6}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{111}\! \left(x \right) = F_{1}\! \left(x \right)+F_{112}\! \left(x \right)+F_{30}\! \left(x \right)+F_{6}\! \left(x \right)
F_{112}\! \left(x \right) = F_{111}\! \left(x \right) F_{12}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{12}\! \left(x \right)
F_{114}\! \left(x \right) = F_{1}\! \left(x \right)+F_{112}\! \left(x \right)+F_{115}\! \left(x \right)+F_{120}\! \left(x \right)+F_{126}\! \left(x \right)+F_{6}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{12}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{119}\! \left(x \right)
F_{118}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{1}\! \left(x \right)+F_{115}\! \left(x \right)
F_{119}\! \left(x \right) = F_{7}\! \left(x \right)
F_{120}\! \left(x \right) = F_{12}\! \left(x \right) F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{1}\! \left(x \right)+F_{112}\! \left(x \right)+F_{115}\! \left(x \right)+F_{120}\! \left(x \right)+F_{122}\! \left(x \right)+F_{6}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{12}\! \left(x \right) F_{124}\! \left(x \right) F_{14}\! \left(x \right)
F_{124}\! \left(x \right) = F_{1}\! \left(x \right)+F_{112}\! \left(x \right)+F_{115}\! \left(x \right)+F_{125}\! \left(x \right)+F_{6}\! \left(x \right)
F_{125}\! \left(x \right) = F_{12}\! \left(x \right) F_{124}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{12}\! \left(x \right) F_{124}\! \left(x \right) F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{1}\! \left(x \right)+F_{129}\! \left(x \right)+F_{130}\! \left(x \right)
F_{129}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{12}\! \left(x \right) F_{128}\! \left(x \right) F_{52}\! \left(x \right)
F_{132}\! \left(x \right) = F_{12}\! \left(x \right) F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{1}\! \left(x \right)+F_{134}\! \left(x \right)+F_{19}\! \left(x \right)+F_{21}\! \left(x \right)
F_{134}\! \left(x \right) = F_{12}\! \left(x \right) F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{1}\! \left(x \right)+F_{115}\! \left(x \right)+F_{136}\! \left(x \right)+F_{206}\! \left(x \right)+F_{34}\! \left(x \right)
F_{136}\! \left(x \right) = F_{12}\! \left(x \right) F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{1}\! \left(x \right)+F_{138}\! \left(x \right)+F_{149}\! \left(x \right)+F_{202}\! \left(x \right)+F_{204}\! \left(x \right)
F_{138}\! \left(x \right) = F_{12}\! \left(x \right) F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{1}\! \left(x \right)+F_{140}\! \left(x \right)+F_{144}\! \left(x \right)+F_{145}\! \left(x \right)+F_{34}\! \left(x \right)+F_{44}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{12}\! \left(x \right) F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{33}\! \left(x \right)
F_{143}\! \left(x \right) = 2 F_{44}\! \left(x \right)+F_{1}\! \left(x \right)+F_{140}\! \left(x \right)+F_{34}\! \left(x \right)
F_{144}\! \left(x \right) = F_{12}\! \left(x \right) F_{139}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{1}\! \left(x \right)+F_{140}\! \left(x \right)+F_{148}\! \left(x \right)+F_{34}\! \left(x \right)+F_{44}\! \left(x \right)
F_{148}\! \left(x \right) = F_{12}\! \left(x \right) F_{147}\! \left(x \right)
F_{149}\! \left(x \right) = F_{12}\! \left(x \right) F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{161}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{78}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{157}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{53}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{12}\! \left(x \right) F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{15}\! \left(x \right)+F_{154}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{56}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{12}\! \left(x \right) F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{158}\! \left(x \right)+F_{80}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{184}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{167}\! \left(x \right)
F_{163}\! \left(x \right) = F_{15}\! \left(x \right)+F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{12}\! \left(x \right) F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{15}\! \left(x \right)+F_{164}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)+F_{176}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{171}\! \left(x \right)+F_{62}\! \left(x \right)
F_{169}\! \left(x \right) = F_{12}\! \left(x \right) F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{168}\! \left(x \right)+F_{53}\! \left(x \right)
F_{171}\! \left(x \right) = F_{12}\! \left(x \right) F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = F_{15}\! \left(x \right)+F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{12}\! \left(x \right) F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{173}\! \left(x \right)+F_{53}\! \left(x \right)
F_{176}\! \left(x \right) = 2 F_{62}\! \left(x \right)+F_{177}\! \left(x \right)+F_{179}\! \left(x \right)
F_{177}\! \left(x \right) = F_{12}\! \left(x \right) F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = F_{176}\! \left(x \right)+F_{80}\! \left(x \right)
F_{179}\! \left(x \right) = F_{12}\! \left(x \right) F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{164}\! \left(x \right)+F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{12}\! \left(x \right) F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{181}\! \left(x \right)+F_{80}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{191}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)+F_{61}\! \left(x \right)
F_{186}\! \left(x \right) = 2 F_{62}\! \left(x \right)+F_{187}\! \left(x \right)+F_{189}\! \left(x \right)
F_{187}\! \left(x \right) = F_{12}\! \left(x \right) F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = F_{154}\! \left(x \right)+F_{186}\! \left(x \right)
F_{189}\! \left(x \right) = F_{12}\! \left(x \right) F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{164}\! \left(x \right)+F_{186}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)+F_{197}\! \left(x \right)
F_{192}\! \left(x \right) = 2 F_{62}\! \left(x \right)+F_{193}\! \left(x \right)+F_{195}\! \left(x \right)
F_{193}\! \left(x \right) = F_{12}\! \left(x \right) F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{192}\! \left(x \right)+F_{56}\! \left(x \right)
F_{195}\! \left(x \right) = F_{12}\! \left(x \right) F_{196}\! \left(x \right)
F_{196}\! \left(x \right) = F_{168}\! \left(x \right)+F_{192}\! \left(x \right)
F_{197}\! \left(x \right) = 3 F_{62}\! \left(x \right)+F_{198}\! \left(x \right)+F_{200}\! \left(x \right)
F_{198}\! \left(x \right) = F_{12}\! \left(x \right) F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = F_{158}\! \left(x \right)+F_{197}\! \left(x \right)
F_{200}\! \left(x \right) = F_{12}\! \left(x \right) F_{201}\! \left(x \right)
F_{201}\! \left(x \right) = F_{176}\! \left(x \right)+F_{197}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{78}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right)
F_{205}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{52}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = F_{12}\! \left(x \right) F_{128}\! \left(x \right) F_{208}\! \left(x \right)
F_{208}\! \left(x \right) = F_{1}\! \left(x \right)+F_{209}\! \left(x \right)+F_{210}\! \left(x \right)+F_{215}\! \left(x \right)
F_{209}\! \left(x \right) = F_{12}\! \left(x \right) F_{147}\! \left(x \right)
F_{210}\! \left(x \right) = F_{12}\! \left(x \right) F_{211}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)+F_{51}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right)+F_{214}\! \left(x \right)
F_{213}\! \left(x \right) = F_{15}\! \left(x \right)+F_{168}\! \left(x \right)
F_{214}\! \left(x \right) = F_{192}\! \left(x \right)+F_{61}\! \left(x \right)
F_{215}\! \left(x \right) = F_{216}\! \left(x \right)
F_{216}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{52}\! \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_12(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_132(x) + F_4(x))
Eq(F_4(x), F_12(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_17(x) + F_4(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_14(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_8(x))
Eq(F_12(x), x)
Eq(F_13(x), F_10(x)*F_14(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_12(x)*F_14(x))
Eq(F_17(x), F_12(x)*F_18(x))
Eq(F_18(x), F_1(x) + F_107(x) + F_113(x) + F_19(x) + F_6(x))
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_1(x) + F_105(x) + F_19(x) + F_21(x) + F_6(x))
Eq(F_21(x), F_12(x)*F_22(x))
Eq(F_22(x), F_1(x) + F_103(x) + F_23(x) + F_76(x))
Eq(F_23(x), F_12(x)*F_24(x))
Eq(F_24(x), F_1(x) + F_25(x) + F_27(x) + F_35(x) + F_74(x))
Eq(F_25(x), F_12(x)*F_26(x))
Eq(F_26(x), F_1(x) + F_25(x) + F_27(x) + F_35(x) + F_36(x) + F_6(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_12(x)*F_14(x)*F_29(x))
Eq(F_29(x), F_1(x) + F_30(x) + F_34(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_12(x)*F_32(x))
Eq(F_32(x), F_29(x) + F_33(x))
Eq(F_33(x), F_12(x)*F_14(x)*F_29(x))
Eq(F_34(x), F_12(x)*F_29(x))
Eq(F_35(x), F_12(x)*F_24(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_12(x)*F_14(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_49(x) + F_72(x) + F_9(x))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_33(x) + F_41(x))
Eq(F_41(x), F_1(x) + F_34(x) + F_42(x) + F_44(x) + F_48(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_12(x)*F_40(x))
Eq(F_44(x), F_12(x)*F_45(x))
Eq(F_45(x), F_1(x) + F_34(x) + F_44(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_12(x)*F_38(x))
Eq(F_48(x), F_12(x)*F_41(x))
Eq(F_49(x), F_12(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_59(x))
Eq(F_51(x), F_52(x) + F_55(x))
Eq(F_52(x), F_1(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_12(x)*F_52(x))
Eq(F_55(x), F_53(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_12(x)*F_58(x))
Eq(F_58(x), F_53(x) + F_56(x))
Eq(F_59(x), F_60(x) + F_66(x))
Eq(F_60(x), F_15(x) + F_61(x))
Eq(F_61(x), F_62(x) + F_63(x) + F_65(x))
Eq(F_62(x), 0)
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_53(x) + F_61(x))
Eq(F_65(x), F_12(x)*F_60(x))
Eq(F_66(x), F_61(x) + F_67(x))
Eq(F_67(x), 2*F_62(x) + F_68(x) + F_70(x))
Eq(F_68(x), F_12(x)*F_69(x))
Eq(F_69(x), F_56(x) + F_67(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_61(x) + F_67(x))
Eq(F_72(x), F_12(x)*F_73(x))
Eq(F_73(x), F_52(x) + F_60(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_12(x)*F_14(x)*F_45(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_86(x))
Eq(F_78(x), F_14(x) + F_79(x))
Eq(F_79(x), F_53(x) + F_80(x))
Eq(F_80(x), F_62(x) + F_81(x) + F_83(x))
Eq(F_81(x), F_12(x)*F_82(x))
Eq(F_82(x), F_15(x) + F_80(x))
Eq(F_83(x), F_12(x)*F_84(x))
Eq(F_84(x), F_53(x) + F_85(x))
Eq(F_85(x), F_83(x))
Eq(F_86(x), F_87(x) + F_94(x))
Eq(F_87(x), F_15(x) + F_88(x))
Eq(F_88(x), F_62(x) + F_89(x) + F_91(x))
Eq(F_89(x), F_12(x)*F_90(x))
Eq(F_90(x), F_15(x) + F_88(x))
Eq(F_91(x), F_12(x)*F_92(x))
Eq(F_92(x), F_15(x) + F_93(x))
Eq(F_93(x), F_91(x))
Eq(F_94(x), F_61(x) + F_95(x))
Eq(F_95(x), F_100(x) + F_62(x) + F_96(x) + F_98(x))
Eq(F_96(x), F_12(x)*F_97(x))
Eq(F_97(x), F_80(x) + F_95(x))
Eq(F_98(x), F_12(x)*F_99(x))
Eq(F_99(x), F_88(x) + F_95(x))
Eq(F_100(x), F_101(x)*F_12(x))
Eq(F_101(x), F_102(x) + F_61(x))
Eq(F_102(x), F_100(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_12(x)*F_14(x)*F_73(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_12(x)*F_14(x)*F_32(x))
Eq(F_107(x), F_108(x)*F_12(x))
Eq(F_108(x), F_1(x) + F_107(x) + F_109(x) + F_19(x) + F_6(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_111(x)*F_12(x)*F_14(x))
Eq(F_111(x), F_1(x) + F_112(x) + F_30(x) + F_6(x))
Eq(F_112(x), F_111(x)*F_12(x))
Eq(F_113(x), F_114(x)*F_12(x))
Eq(F_114(x), F_1(x) + F_112(x) + F_115(x) + F_120(x) + F_126(x) + F_6(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_12(x))
Eq(F_117(x), F_118(x) + F_119(x))
Eq(F_118(x), F_1(x) + F_115(x) + 2*F_34(x))
Eq(F_119(x), F_7(x))
Eq(F_120(x), F_12(x)*F_121(x))
Eq(F_121(x), F_1(x) + F_112(x) + F_115(x) + F_120(x) + F_122(x) + F_6(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_12(x)*F_124(x)*F_14(x))
Eq(F_124(x), F_1(x) + F_112(x) + F_115(x) + F_125(x) + F_6(x))
Eq(F_125(x), F_12(x)*F_124(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_12(x)*F_124(x)*F_128(x))
Eq(F_128(x), F_1(x) + F_129(x) + F_130(x))
Eq(F_129(x), F_12(x)*F_78(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_12(x)*F_128(x)*F_52(x))
Eq(F_132(x), F_12(x)*F_133(x))
Eq(F_133(x), F_1(x) + F_134(x) + F_19(x) + F_21(x))
Eq(F_134(x), F_12(x)*F_135(x))
Eq(F_135(x), F_1(x) + F_115(x) + F_136(x) + F_206(x) + F_34(x))
Eq(F_136(x), F_12(x)*F_137(x))
Eq(F_137(x), F_1(x) + F_138(x) + F_149(x) + F_202(x) + F_204(x))
Eq(F_138(x), F_12(x)*F_139(x))
Eq(F_139(x), F_1(x) + F_140(x) + F_144(x) + F_145(x) + F_34(x) + F_44(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_12(x)*F_142(x))
Eq(F_142(x), F_143(x) + F_33(x))
Eq(F_143(x), F_1(x) + F_140(x) + F_34(x) + 2*F_44(x))
Eq(F_144(x), F_12(x)*F_139(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_12(x)*F_14(x)*F_147(x))
Eq(F_147(x), F_1(x) + F_140(x) + F_148(x) + F_34(x) + F_44(x))
Eq(F_148(x), F_12(x)*F_147(x))
Eq(F_149(x), F_12(x)*F_150(x))
Eq(F_150(x), F_151(x) + F_161(x))
Eq(F_151(x), F_152(x) + F_78(x))
Eq(F_152(x), F_153(x) + F_157(x))
Eq(F_153(x), F_154(x) + F_53(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_12(x)*F_156(x))
Eq(F_156(x), F_15(x) + F_154(x))
Eq(F_157(x), F_158(x) + F_56(x))
Eq(F_158(x), F_159(x))
Eq(F_159(x), F_12(x)*F_160(x))
Eq(F_160(x), F_158(x) + F_80(x))
Eq(F_161(x), F_162(x) + F_184(x))
Eq(F_162(x), F_163(x) + F_167(x))
Eq(F_163(x), F_15(x) + F_164(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_12(x)*F_166(x))
Eq(F_166(x), F_15(x) + F_164(x))
Eq(F_167(x), F_168(x) + F_176(x))
Eq(F_168(x), F_169(x) + F_171(x) + F_62(x))
Eq(F_169(x), F_12(x)*F_170(x))
Eq(F_170(x), F_168(x) + F_53(x))
Eq(F_171(x), F_12(x)*F_172(x))
Eq(F_172(x), F_15(x) + F_173(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_12(x)*F_175(x))
Eq(F_175(x), F_173(x) + F_53(x))
Eq(F_176(x), F_177(x) + F_179(x) + 2*F_62(x))
Eq(F_177(x), F_12(x)*F_178(x))
Eq(F_178(x), F_176(x) + F_80(x))
Eq(F_179(x), F_12(x)*F_180(x))
Eq(F_180(x), F_164(x) + F_181(x))
Eq(F_181(x), F_182(x))
Eq(F_182(x), F_12(x)*F_183(x))
Eq(F_183(x), F_181(x) + F_80(x))
Eq(F_184(x), F_185(x) + F_191(x))
Eq(F_185(x), F_186(x) + F_61(x))
Eq(F_186(x), F_187(x) + F_189(x) + 2*F_62(x))
Eq(F_187(x), F_12(x)*F_188(x))
Eq(F_188(x), F_154(x) + F_186(x))
Eq(F_189(x), F_12(x)*F_190(x))
Eq(F_190(x), F_164(x) + F_186(x))
Eq(F_191(x), F_192(x) + F_197(x))
Eq(F_192(x), F_193(x) + F_195(x) + 2*F_62(x))
Eq(F_193(x), F_12(x)*F_194(x))
Eq(F_194(x), F_192(x) + F_56(x))
Eq(F_195(x), F_12(x)*F_196(x))
Eq(F_196(x), F_168(x) + F_192(x))
Eq(F_197(x), F_198(x) + F_200(x) + 3*F_62(x))
Eq(F_198(x), F_12(x)*F_199(x))
Eq(F_199(x), F_158(x) + F_197(x))
Eq(F_200(x), F_12(x)*F_201(x))
Eq(F_201(x), F_176(x) + F_197(x))
Eq(F_202(x), F_203(x))
Eq(F_203(x), F_12(x)*F_14(x)*F_78(x))
Eq(F_204(x), F_205(x))
Eq(F_205(x), F_12(x)*F_14(x)*F_52(x))
Eq(F_206(x), F_207(x))
Eq(F_207(x), F_12(x)*F_128(x)*F_208(x))
Eq(F_208(x), F_1(x) + F_209(x) + F_210(x) + F_215(x))
Eq(F_209(x), F_12(x)*F_147(x))
Eq(F_210(x), F_12(x)*F_211(x))
Eq(F_211(x), F_212(x) + F_51(x))
Eq(F_212(x), F_213(x) + F_214(x))
Eq(F_213(x), F_15(x) + F_168(x))
Eq(F_214(x), F_192(x) + F_61(x))
Eq(F_215(x), F_216(x))
Eq(F_216(x), F_12(x)*F_14(x)*F_52(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "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": "row_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"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]]}]]}], "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": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": 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