0123_0231_0312_0321
Counting sequence:
1, 1, 2, 6, 20, 69, 241, 846, 2977, 10490, 36994, 130532, 460737, 1626629, 5743674, 20283121, 71632290, 252989326, 893528468, 3155899165, 11146628105, 39370204614, 139057473905, 491159630010, 1734810719530, 6127485120996, 21642773880217, 76444087911869, 270007047670258, 953688268694945, 3368510271049218, 11897874255711062, 42024341363518356, 148433690150759797, 524280942888604641, 1851806787338308030, 6540745928183166209, 23102495425942829626, 81600065989346789906, 288218683030778439012, 1018013999706492354545, 3595715916951294966069, 12700388187380117044522, 44858899871425539927057, 158445621459083481127714, 559644018099051144467294, 1976712415333981076581396, 6981923950571509640410445, 24660775983522279297697401, 87104052761324070099071798, 307659256666815416555564625, 1086679841132498147739438970, 3838249789554974207535623994, 13557039423804177332114357860, 47884668277962794272604970185, 169132904643094143854136224365, 597392452780703892003486972386, 2110043243174338851606300785217, 7452860288662792225460558184194, 26324164996188407580310129010598, 92979290622339654304322051191060, 328411119057005049828601704235173, 1159977263737161817813021893702097, 4097142801532265112725038075287086, 14471472554616139365861633112638817, 51114527377643611998457477891951226, 180541054075848682810715207413245090, 637687050610915728244035576564548324, 2252367344360499836166234070560035361, 7955561664740606145611799441692522341, 28099750939810054076418725591679364122, 99250818000555368984172392645403519025, 350562711209782333362877624988999359394, 1238218656193505733396132941717043849262, 4373498354273548769095071418046672380052, 15447584931109523347368109657815638996349, 54562243054388706895749148126190826406889, 192718692300620080017276973254850879854246, 680699551245331641389287616051203480459825, 2404291319820797835075982085139753790477626, 8492170650017422317969580939632542298581578, 29995101572962685033522934487588673157650660, 105945364907440107174487360553978912049147385, 374208445937993900063187333875207956174609949, 1321737493033965120842260692753026201762983890, 4668494309669285731659365512195264517055561185, 16489536866648022202439034172269559242641122050, 58242509905898526750542176116613001004109665526, 205717721945228246412961114661447237357943455892, 726613279384930759925326137091435974353314867669, 2566462688708428868585848966712203710902507768513, 9064974339731424618600119681111745733593156257950, 32018295119397618654253403523352076977789682498753, 113091464347511319226705192976818953975302196439482, 399449104350220772090550645831856776785299192406066, 1410889742093120378157210541723122151911865068979812, 4983387977754246639355012630828840874378799878663761, 17601769292037617204805731555296802655851312843570325, 62171013694530603852796486196044370217610543222427914, 219593546516599314912882345809423838277380243621098321, 775623925140858072006931430647440500361637885568309026
Generating function in Maple syntax:
-(x^4+3*x^3-10*x^2+6*x-1)/(x-1)/(x^3-9*x^2+6*x-1)
Generating function in latex syntax:
-\frac{x^{4}+3 x^{3}-10 x^{2}+6 x -1}{\left(x -1\right) \left(x^{3}-9 x^{2}+6 x -1\right)}
Generating function in sympy syntax:
(-x**4 - 3*x**3 + 10*x**2 - 6*x + 1)/((x - 1)*(x**3 - 9*x**2 + 6*x - 1))
Implicit equation for the generating function in Maple syntax:
(x-1)*(x^3-9*x^2+6*x-1)*F(x)+x^4+3*x^3-10*x^2+6*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(x^{3}-9 x^{2}+6 x -1\right) F \! \left(x \right)+x^{4}+3 x^{3}-10 x^{2}+6 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/3528*((30*I*3^(1/2)-32)*(148+4*I*3^(1/2))^(2/3)-154*I*(148+4*I*3^(1/2))^(1/3)*3^(1/2)-182*(148+4*I*3^(1/2))^(1/3)+1960)*(1/392*(19*I*3^(1/2)-17)*(148+4*I*3^(1/2))^(2/3)-1/4*I*3^(1/2)*(148+4*I*3^(1/2))^(1/3)-1/4*(148+4*I*3^(1/2))^(1/3)+3)^(-n)+1/3528*((-31*I*3^(1/2)-29)*(148+4*I*3^(1/2))^(2/3)+168*I*(148+4*I*3^(1/2))^(1/3)*3^(1/2)-140*(148+4*I*3^(1/2))^(1/3)+1960)*(1/196*(-9*I*3^(1/2)-10)*(148+4*I*3^(1/2))^(2/3)+1/4*I*3^(1/2)*(148+4*I*3^(1/2))^(1/3)-1/4*(148+4*I*3^(1/2))^(1/3)+3)^(-n)+1/3+1/3528*((I*3^(1/2)+61)*(148+4*I*3^(1/2))^(2/3)-14*I*(148+4*I*3^(1/2))^(1/3)*3^(1/2)+322*(148+4*I*3^(1/2))^(1/3)+1960)*(1/2*(148+4*I*3^(1/2))^(1/3)+3+37/392*(148+4*I*3^(1/2))^(2/3)-1/392*I*3^(1/2)*(148+4*I*3^(1/2))^(2/3))^(-n))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(\left(30 \,\mathrm{I} \sqrt{3}-32\right) \left(148+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}}-154 \,\mathrm{I} \left(148+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}} \sqrt{3}-182 \left(148+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}+1960\right) \left(\frac{\left(19 \,\mathrm{I} \sqrt{3}-17\right) \left(148+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}}}{392}-\frac{\mathrm{I} \sqrt{3}\, \left(148+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}}{4}-\frac{\left(148+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}}{4}+3\right)^{-n}}{3528}\\+\\\frac{\left(\left(-31 \,\mathrm{I} \sqrt{3}-29\right) \left(148+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}}+168 \,\mathrm{I} \left(148+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}} \sqrt{3}-140 \left(148+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}+1960\right) \left(\frac{\left(-9 \,\mathrm{I} \sqrt{3}-10\right) \left(148+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}}}{196}+\frac{\mathrm{I} \sqrt{3}\, \left(148+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}}{4}-\frac{\left(148+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}}{4}+3\right)^{-n}}{3528}\\+\frac{1}{3}+\\\frac{\left(\left(\mathrm{I} \sqrt{3}+61\right) \left(148+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}}-14 \,\mathrm{I} \left(148+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}} \sqrt{3}+322 \left(148+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}+1960\right) \left(\frac{\left(148+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}}{2}+3+\frac{37 \left(148+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}}}{392}-\frac{\mathrm{I} \sqrt{3}\, \left(148+4 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}}}{392}\right)^{-n}}{3528} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(n+3) = a(n)-9*a(n+1)+6*a(n+2)+1, n >= 5
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) = 20
a \! \left(n +3\right) = a \! \left(n \right)-9 a \! \left(n +1\right)+6 a \! \left(n +2\right)+1, \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14952/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[17,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[4,x]
F[14,x] = F[15,x]+F[4,x]
F[15,x] = F[16,x]
F[16,x] = F[11,x]*F[4,x]
F[17,x] = F[18,x]+F[2,x]
F[18,x] = F[19,x]+F[20,x]+F[265,x]
F[19,x] = 0
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[35,x]
F[22,x] = F[23,x]+F[7,x]
F[23,x] = F[19,x]+F[24,x]+F[33,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[26,x]+F[30,x]
F[26,x] = F[11,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[4,x]
F[30,x] = F[15,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[27,x]*F[4,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[14,x]
F[35,x] = F[18,x]+F[36,x]
F[36,x] = F[19,x]+F[256,x]+F[262,x]+F[37,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]+F[48,x]
F[39,x] = F[23,x]+F[40,x]
F[40,x] = F[19,x]+F[41,x]+F[45,x]+F[47,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[27,x]
F[44,x] = F[31,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[30,x]
F[47,x] = 0
F[48,x] = F[36,x]+F[49,x]
F[49,x] = F[19,x]+F[214,x]+F[261,x]+F[50,x]+F[99,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[56,x]
F[52,x] = F[40,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[44,x]
F[56,x] = F[49,x]+F[57,x]
F[57,x] = F[19,x]+F[212,x]+F[213,x]+F[58,x]+F[62,x]+F[63,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[60,x]+F[61,x]
F[60,x] = F[53,x]
F[61,x] = F[57,x]
F[62,x] = 0
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[66,x]
F[66,x] = 3*F[19,x]+F[67,x]+F[80,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[72,x]
F[69,x] = F[31,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[31,x]*F[4,x]
F[72,x] = F[66,x]+F[73,x]
F[73,x] = 3*F[19,x]+F[74,x]+F[78,x]+F[79,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[70,x]
F[77,x] = F[73,x]
F[78,x] = 0
F[79,x] = F[4,x]*F[66,x]
F[80,x] = F[4,x]*F[81,x]
F[81,x] = 2*F[19,x]+F[103,x]+F[82,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[84,x]+F[86,x]
F[84,x] = F[27,x]+F[85,x]
F[85,x] = F[41,x]
F[86,x] = F[81,x]+F[87,x]
F[87,x] = 2*F[19,x]+F[102,x]+F[88,x]+F[99,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[90,x]+F[92,x]
F[90,x] = F[85,x]+F[91,x]
F[91,x] = F[54,x]
F[92,x] = F[87,x]+F[93,x]
F[93,x] = 2*F[19,x]+F[62,x]+F[63,x]+F[94,x]+F[98,x]
F[94,x] = F[4,x]*F[95,x]
F[95,x] = F[96,x]+F[97,x]
F[96,x] = F[91,x]
F[97,x] = F[93,x]
F[98,x] = 0
F[99,x] = F[100,x]*F[4,x]
F[100,x] = F[101,x]+F[65,x]
F[101,x] = F[81,x]
F[102,x] = 0
F[103,x] = F[104,x]*F[4,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]+F[19,x]+F[211,x]
F[106,x] = F[107,x]*F[4,x]
F[107,x] = F[108,x]+F[120,x]
F[108,x] = F[109,x]+F[4,x]
F[109,x] = F[110,x]+F[114,x]+F[19,x]
F[110,x] = F[111,x]*F[4,x]
F[111,x] = F[112,x]+F[115,x]
F[112,x] = F[113,x]+F[4,x]
F[113,x] = F[114,x]
F[114,x] = x^2
F[115,x] = F[116,x]+F[118,x]
F[116,x] = F[117,x]
F[117,x] = x^2
F[118,x] = F[119,x]
F[119,x] = F[113,x]*F[4,x]
F[120,x] = F[105,x]+F[121,x]
F[121,x] = F[122,x]+F[188,x]+F[19,x]+F[208,x]
F[122,x] = F[123,x]*F[4,x]
F[123,x] = F[124,x]+F[133,x]
F[124,x] = F[109,x]+F[125,x]
F[125,x] = F[126,x]+F[130,x]+F[132,x]+F[19,x]
F[126,x] = F[127,x]*F[4,x]
F[127,x] = F[128,x]+F[129,x]
F[128,x] = F[113,x]
F[129,x] = F[118,x]
F[130,x] = F[131,x]*F[4,x]
F[131,x] = F[115,x]
F[132,x] = 0
F[133,x] = F[121,x]+F[134,x]
F[134,x] = F[135,x]+F[184,x]+F[187,x]+F[19,x]+F[190,x]
F[135,x] = F[136,x]*F[4,x]
F[136,x] = F[137,x]+F[141,x]
F[137,x] = F[125,x]+F[138,x]
F[138,x] = F[139,x]
F[139,x] = F[140,x]*F[4,x]
F[140,x] = F[129,x]
F[141,x] = F[134,x]+F[142,x]
F[142,x] = F[143,x]+F[147,x]+F[148,x]+F[183,x]+F[189,x]+F[19,x]
F[143,x] = F[144,x]*F[4,x]
F[144,x] = F[145,x]+F[146,x]
F[145,x] = F[138,x]
F[146,x] = F[142,x]
F[147,x] = 0
F[148,x] = F[149,x]*F[4,x]
F[149,x] = F[150,x]
F[150,x] = F[151,x]
F[151,x] = 3*F[19,x]+F[152,x]+F[165,x]
F[152,x] = F[153,x]*F[4,x]
F[153,x] = F[154,x]+F[157,x]
F[154,x] = F[118,x]+F[155,x]
F[155,x] = F[156,x]
F[156,x] = F[118,x]*F[4,x]
F[157,x] = F[151,x]+F[158,x]
F[158,x] = 3*F[19,x]+F[159,x]+F[163,x]+F[164,x]
F[159,x] = F[160,x]*F[4,x]
F[160,x] = F[161,x]+F[162,x]
F[161,x] = F[155,x]
F[162,x] = F[158,x]
F[163,x] = 0
F[164,x] = F[151,x]*F[4,x]
F[165,x] = F[166,x]*F[4,x]
F[166,x] = 2*F[19,x]+F[167,x]+F[188,x]
F[167,x] = F[168,x]*F[4,x]
F[168,x] = F[169,x]+F[171,x]
F[169,x] = F[113,x]+F[170,x]
F[170,x] = F[126,x]
F[171,x] = F[166,x]+F[172,x]
F[172,x] = 2*F[19,x]+F[173,x]+F[184,x]+F[187,x]
F[173,x] = F[174,x]*F[4,x]
F[174,x] = F[175,x]+F[177,x]
F[175,x] = F[170,x]+F[176,x]
F[176,x] = F[139,x]
F[177,x] = F[172,x]+F[178,x]
F[178,x] = 2*F[19,x]+F[147,x]+F[148,x]+F[179,x]+F[183,x]
F[179,x] = F[180,x]*F[4,x]
F[180,x] = F[181,x]+F[182,x]
F[181,x] = F[176,x]
F[182,x] = F[178,x]
F[183,x] = 0
F[184,x] = F[185,x]*F[4,x]
F[185,x] = F[150,x]+F[186,x]
F[186,x] = F[166,x]
F[187,x] = 0
F[188,x] = F[105,x]*F[4,x]
F[189,x] = 0
F[190,x] = F[191,x]*F[4,x]
F[191,x] = F[192,x]
F[192,x] = F[151,x]+F[193,x]
F[193,x] = 2*F[19,x]+F[194,x]+F[207,x]
F[194,x] = F[195,x]*F[4,x]
F[195,x] = F[196,x]+F[199,x]
F[196,x] = F[116,x]+F[197,x]
F[197,x] = F[198,x]
F[198,x] = F[116,x]*F[4,x]
F[199,x] = F[193,x]+F[200,x]
F[200,x] = 2*F[19,x]+F[201,x]+F[205,x]+F[206,x]
F[201,x] = F[202,x]*F[4,x]
F[202,x] = F[203,x]+F[204,x]
F[203,x] = F[197,x]
F[204,x] = F[200,x]
F[205,x] = 0
F[206,x] = F[193,x]*F[4,x]
F[207,x] = F[105,x]*F[4,x]
F[208,x] = F[209,x]*F[4,x]
F[209,x] = F[192,x]+F[210,x]
F[210,x] = F[105,x]+F[166,x]
F[211,x] = F[2,x]*F[4,x]
F[212,x] = 0
F[213,x] = 0
F[214,x] = F[215,x]*F[4,x]
F[215,x] = F[216,x]
F[216,x] = F[217,x]+F[66,x]
F[217,x] = 2*F[19,x]+F[218,x]+F[231,x]
F[218,x] = F[219,x]*F[4,x]
F[219,x] = F[220,x]+F[223,x]
F[220,x] = F[15,x]+F[221,x]
F[221,x] = F[222,x]
F[222,x] = F[15,x]*F[4,x]
F[223,x] = F[217,x]+F[224,x]
F[224,x] = 2*F[19,x]+F[225,x]+F[229,x]+F[230,x]
F[225,x] = F[226,x]*F[4,x]
F[226,x] = F[227,x]+F[228,x]
F[227,x] = F[221,x]
F[228,x] = F[224,x]
F[229,x] = 0
F[230,x] = F[217,x]*F[4,x]
F[231,x] = F[232,x]*F[4,x]
F[232,x] = F[19,x]+F[233,x]+F[259,x]
F[233,x] = F[234,x]*F[4,x]
F[234,x] = F[235,x]+F[237,x]
F[235,x] = F[11,x]+F[236,x]
F[236,x] = F[19,x]+F[24,x]+F[28,x]
F[237,x] = F[232,x]+F[238,x]
F[238,x] = F[103,x]+F[19,x]+F[239,x]+F[256,x]
F[239,x] = F[240,x]*F[4,x]
F[240,x] = F[241,x]+F[244,x]
F[241,x] = F[236,x]+F[242,x]
F[242,x] = F[19,x]+F[243,x]+F[41,x]+F[45,x]
F[243,x] = 0
F[244,x] = F[238,x]+F[245,x]
F[245,x] = F[102,x]+F[19,x]+F[214,x]+F[246,x]+F[99,x]
F[246,x] = F[247,x]*F[4,x]
F[247,x] = F[248,x]+F[250,x]
F[248,x] = F[242,x]+F[249,x]
F[249,x] = F[54,x]
F[250,x] = F[245,x]+F[251,x]
F[251,x] = F[19,x]+F[212,x]+F[252,x]+F[62,x]+F[63,x]+F[98,x]
F[252,x] = F[253,x]*F[4,x]
F[253,x] = F[254,x]+F[255,x]
F[254,x] = F[249,x]
F[255,x] = F[251,x]
F[256,x] = F[257,x]*F[4,x]
F[257,x] = F[216,x]+F[258,x]
F[258,x] = F[232,x]+F[81,x]
F[259,x] = F[260,x]*F[4,x]
F[260,x] = F[105,x]+F[2,x]
F[261,x] = 0
F[262,x] = F[263,x]*F[4,x]
F[263,x] = F[264,x]
F[264,x] = F[105,x]+F[217,x]
F[265,x] = F[266,x]*F[4,x]
F[266,x] = F[264,x]+F[267,x]
F[267,x] = F[2,x]+F[232,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{17}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \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_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{2}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{265}\! \left(x \right)
F_{19}\! \left(x \right) = 0
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{35}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{7}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)+F_{33}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{30}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{15}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{14}\! \left(x \right)
F_{35}\! \left(x \right) = F_{18}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{19}\! \left(x \right)+F_{256}\! \left(x \right)+F_{262}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{48}\! \left(x \right)
F_{39}\! \left(x \right) = F_{23}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{19}\! \left(x \right)+F_{41}\! \left(x \right)+F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{27}\! \left(x \right)
F_{44}\! \left(x \right) = F_{31}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{30}\! \left(x \right)
F_{47}\! \left(x \right) = 0
F_{48}\! \left(x \right) = F_{36}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{19}\! \left(x \right)+F_{214}\! \left(x \right)+F_{261}\! \left(x \right)+F_{50}\! \left(x \right)+F_{99}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{56}\! \left(x \right)
F_{52}\! \left(x \right) = F_{40}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{44}\! \left(x \right)
F_{56}\! \left(x \right) = F_{49}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{19}\! \left(x \right)+F_{212}\! \left(x \right)+F_{213}\! \left(x \right)+F_{58}\! \left(x \right)+F_{62}\! \left(x \right)+F_{63}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{61}\! \left(x \right)
F_{60}\! \left(x \right) = F_{53}\! \left(x \right)
F_{61}\! \left(x \right) = F_{57}\! \left(x \right)
F_{62}\! \left(x \right) = 0
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = 3 F_{19}\! \left(x \right)+F_{67}\! \left(x \right)+F_{80}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{72}\! \left(x \right)
F_{69}\! \left(x \right) = F_{31}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{72}\! \left(x \right) = F_{66}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = 3 F_{19}\! \left(x \right)+F_{74}\! \left(x \right)+F_{78}\! \left(x \right)+F_{79}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{77}\! \left(x \right)
F_{76}\! \left(x \right) = F_{70}\! \left(x \right)
F_{77}\! \left(x \right) = F_{73}\! \left(x \right)
F_{78}\! \left(x \right) = 0
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{103}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{86}\! \left(x \right)
F_{84}\! \left(x \right) = F_{27}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{41}\! \left(x \right)
F_{86}\! \left(x \right) = F_{81}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{102}\! \left(x \right)+F_{88}\! \left(x \right)+F_{99}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{92}\! \left(x \right)
F_{90}\! \left(x \right) = F_{85}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{54}\! \left(x \right)
F_{92}\! \left(x \right) = F_{87}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{62}\! \left(x \right)+F_{63}\! \left(x \right)+F_{94}\! \left(x \right)+F_{98}\! \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_{91}\! \left(x \right)
F_{97}\! \left(x \right) = F_{93}\! \left(x \right)
F_{98}\! \left(x \right) = 0
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{4}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{65}\! \left(x \right)
F_{101}\! \left(x \right) = F_{81}\! \left(x \right)
F_{102}\! \left(x \right) = 0
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{19}\! \left(x \right)+F_{211}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{120}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{114}\! \left(x \right)+F_{19}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{4}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{115}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = x^{2}
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{118}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = x^{2}
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{120}\! \left(x \right) = F_{105}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{188}\! \left(x \right)+F_{19}\! \left(x \right)+F_{208}\! \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_{133}\! \left(x \right)
F_{124}\! \left(x \right) = F_{109}\! \left(x \right)+F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{130}\! \left(x \right)+F_{132}\! \left(x \right)+F_{19}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{4}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{129}\! \left(x \right)
F_{128}\! \left(x \right) = F_{113}\! \left(x \right)
F_{129}\! \left(x \right) = F_{118}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{4}\! \left(x \right)
F_{131}\! \left(x \right) = F_{115}\! \left(x \right)
F_{132}\! \left(x \right) = 0
F_{133}\! \left(x \right) = F_{121}\! \left(x \right)+F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{184}\! \left(x \right)+F_{187}\! \left(x \right)+F_{19}\! \left(x \right)+F_{190}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{141}\! \left(x \right)
F_{137}\! \left(x \right) = F_{125}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{4}\! \left(x \right)
F_{140}\! \left(x \right) = F_{129}\! \left(x \right)
F_{141}\! \left(x \right) = F_{134}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{147}\! \left(x \right)+F_{148}\! \left(x \right)+F_{183}\! \left(x \right)+F_{189}\! \left(x \right)+F_{19}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right) F_{4}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{146}\! \left(x \right)
F_{145}\! \left(x \right) = F_{138}\! \left(x \right)
F_{146}\! \left(x \right) = F_{142}\! \left(x \right)
F_{147}\! \left(x \right) = 0
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{4}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = 3 F_{19}\! \left(x \right)+F_{152}\! \left(x \right)+F_{165}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right) F_{4}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{157}\! \left(x \right)
F_{154}\! \left(x \right) = F_{118}\! \left(x \right)+F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{118}\! \left(x \right) F_{4}\! \left(x \right)
F_{157}\! \left(x \right) = F_{151}\! \left(x \right)+F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = 3 F_{19}\! \left(x \right)+F_{159}\! \left(x \right)+F_{163}\! \left(x \right)+F_{164}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right) F_{4}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{162}\! \left(x \right)
F_{161}\! \left(x \right) = F_{155}\! \left(x \right)
F_{162}\! \left(x \right) = F_{158}\! \left(x \right)
F_{163}\! \left(x \right) = 0
F_{164}\! \left(x \right) = F_{151}\! \left(x \right) F_{4}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{4}\! \left(x \right)
F_{166}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{167}\! \left(x \right)+F_{188}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right) F_{4}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{171}\! \left(x \right)
F_{169}\! \left(x \right) = F_{113}\! \left(x \right)+F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{126}\! \left(x \right)
F_{171}\! \left(x \right) = F_{166}\! \left(x \right)+F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{173}\! \left(x \right)+F_{184}\! \left(x \right)+F_{187}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right) F_{4}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)+F_{177}\! \left(x \right)
F_{175}\! \left(x \right) = F_{170}\! \left(x \right)+F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{139}\! \left(x \right)
F_{177}\! \left(x \right) = F_{172}\! \left(x \right)+F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{147}\! \left(x \right)+F_{148}\! \left(x \right)+F_{179}\! \left(x \right)+F_{183}\! \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_{182}\! \left(x \right)
F_{181}\! \left(x \right) = F_{176}\! \left(x \right)
F_{182}\! \left(x \right) = F_{178}\! \left(x \right)
F_{183}\! \left(x \right) = 0
F_{184}\! \left(x \right) = F_{185}\! \left(x \right) F_{4}\! \left(x \right)
F_{185}\! \left(x \right) = F_{150}\! \left(x \right)+F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{166}\! \left(x \right)
F_{187}\! \left(x \right) = 0
F_{188}\! \left(x \right) = F_{105}\! \left(x \right) F_{4}\! \left(x \right)
F_{189}\! \left(x \right) = 0
F_{190}\! \left(x \right) = F_{191}\! \left(x \right) F_{4}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{151}\! \left(x \right)+F_{193}\! \left(x \right)
F_{193}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{194}\! \left(x \right)+F_{207}\! \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_{199}\! \left(x \right)
F_{196}\! \left(x \right) = F_{116}\! \left(x \right)+F_{197}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{116}\! \left(x \right) F_{4}\! \left(x \right)
F_{199}\! \left(x \right) = F_{193}\! \left(x \right)+F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{201}\! \left(x \right)+F_{205}\! \left(x \right)+F_{206}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right) F_{4}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)+F_{204}\! \left(x \right)
F_{203}\! \left(x \right) = F_{197}\! \left(x \right)
F_{204}\! \left(x \right) = F_{200}\! \left(x \right)
F_{205}\! \left(x \right) = 0
F_{206}\! \left(x \right) = F_{193}\! \left(x \right) F_{4}\! \left(x \right)
F_{207}\! \left(x \right) = F_{105}\! \left(x \right) F_{4}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right) F_{4}\! \left(x \right)
F_{209}\! \left(x \right) = F_{192}\! \left(x \right)+F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{105}\! \left(x \right)+F_{166}\! \left(x \right)
F_{211}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{212}\! \left(x \right) = 0
F_{213}\! \left(x \right) = 0
F_{214}\! \left(x \right) = F_{215}\! \left(x \right) F_{4}\! \left(x \right)
F_{215}\! \left(x \right) = F_{216}\! \left(x \right)
F_{216}\! \left(x \right) = F_{217}\! \left(x \right)+F_{66}\! \left(x \right)
F_{217}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{218}\! \left(x \right)+F_{231}\! \left(x \right)
F_{218}\! \left(x \right) = F_{219}\! \left(x \right) F_{4}\! \left(x \right)
F_{219}\! \left(x \right) = F_{220}\! \left(x \right)+F_{223}\! \left(x \right)
F_{220}\! \left(x \right) = F_{15}\! \left(x \right)+F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right)
F_{222}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{223}\! \left(x \right) = F_{217}\! \left(x \right)+F_{224}\! \left(x \right)
F_{224}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{225}\! \left(x \right)+F_{229}\! \left(x \right)+F_{230}\! \left(x \right)
F_{225}\! \left(x \right) = F_{226}\! \left(x \right) F_{4}\! \left(x \right)
F_{226}\! \left(x \right) = F_{227}\! \left(x \right)+F_{228}\! \left(x \right)
F_{227}\! \left(x \right) = F_{221}\! \left(x \right)
F_{228}\! \left(x \right) = F_{224}\! \left(x \right)
F_{229}\! \left(x \right) = 0
F_{230}\! \left(x \right) = F_{217}\! \left(x \right) F_{4}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right) F_{4}\! \left(x \right)
F_{232}\! \left(x \right) = F_{19}\! \left(x \right)+F_{233}\! \left(x \right)+F_{259}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right) F_{4}\! \left(x \right)
F_{234}\! \left(x \right) = F_{235}\! \left(x \right)+F_{237}\! \left(x \right)
F_{235}\! \left(x \right) = F_{11}\! \left(x \right)+F_{236}\! \left(x \right)
F_{236}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)+F_{28}\! \left(x \right)
F_{237}\! \left(x \right) = F_{232}\! \left(x \right)+F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = F_{103}\! \left(x \right)+F_{19}\! \left(x \right)+F_{239}\! \left(x \right)+F_{256}\! \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_{244}\! \left(x \right)
F_{241}\! \left(x \right) = F_{236}\! \left(x \right)+F_{242}\! \left(x \right)
F_{242}\! \left(x \right) = F_{19}\! \left(x \right)+F_{243}\! \left(x \right)+F_{41}\! \left(x \right)+F_{45}\! \left(x \right)
F_{243}\! \left(x \right) = 0
F_{244}\! \left(x \right) = F_{238}\! \left(x \right)+F_{245}\! \left(x \right)
F_{245}\! \left(x \right) = F_{102}\! \left(x \right)+F_{19}\! \left(x \right)+F_{214}\! \left(x \right)+F_{246}\! \left(x \right)+F_{99}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right) F_{4}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right)+F_{250}\! \left(x \right)
F_{248}\! \left(x \right) = F_{242}\! \left(x \right)+F_{249}\! \left(x \right)
F_{249}\! \left(x \right) = F_{54}\! \left(x \right)
F_{250}\! \left(x \right) = F_{245}\! \left(x \right)+F_{251}\! \left(x \right)
F_{251}\! \left(x \right) = F_{19}\! \left(x \right)+F_{212}\! \left(x \right)+F_{252}\! \left(x \right)+F_{62}\! \left(x \right)+F_{63}\! \left(x \right)+F_{98}\! \left(x \right)
F_{252}\! \left(x \right) = F_{253}\! \left(x \right) F_{4}\! \left(x \right)
F_{253}\! \left(x \right) = F_{254}\! \left(x \right)+F_{255}\! \left(x \right)
F_{254}\! \left(x \right) = F_{249}\! \left(x \right)
F_{255}\! \left(x \right) = F_{251}\! \left(x \right)
F_{256}\! \left(x \right) = F_{257}\! \left(x \right) F_{4}\! \left(x \right)
F_{257}\! \left(x \right) = F_{216}\! \left(x \right)+F_{258}\! \left(x \right)
F_{258}\! \left(x \right) = F_{232}\! \left(x \right)+F_{81}\! \left(x \right)
F_{259}\! \left(x \right) = F_{260}\! \left(x \right) F_{4}\! \left(x \right)
F_{260}\! \left(x \right) = F_{105}\! \left(x \right)+F_{2}\! \left(x \right)
F_{261}\! \left(x \right) = 0
F_{262}\! \left(x \right) = F_{263}\! \left(x \right) F_{4}\! \left(x \right)
F_{263}\! \left(x \right) = F_{264}\! \left(x \right)
F_{264}\! \left(x \right) = F_{105}\! \left(x \right)+F_{217}\! \left(x \right)
F_{265}\! \left(x \right) = F_{266}\! \left(x \right) F_{4}\! \left(x \right)
F_{266}\! \left(x \right) = F_{264}\! \left(x \right)+F_{267}\! \left(x \right)
F_{267}\! \left(x \right) = F_{2}\! \left(x \right)+F_{232}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_17(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_4(x))
Eq(F_14(x), F_15(x) + F_4(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_11(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_2(x))
Eq(F_18(x), F_19(x) + F_20(x) + F_265(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_35(x))
Eq(F_22(x), F_23(x) + F_7(x))
Eq(F_23(x), F_19(x) + F_24(x) + F_33(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_26(x) + F_30(x))
Eq(F_26(x), F_11(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_4(x))
Eq(F_30(x), F_15(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_27(x)*F_4(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_14(x))
Eq(F_35(x), F_18(x) + F_36(x))
Eq(F_36(x), F_19(x) + F_256(x) + F_262(x) + F_37(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x) + F_48(x))
Eq(F_39(x), F_23(x) + F_40(x))
Eq(F_40(x), F_19(x) + F_41(x) + F_45(x) + F_47(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_27(x))
Eq(F_44(x), F_31(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_30(x))
Eq(F_47(x), 0)
Eq(F_48(x), F_36(x) + F_49(x))
Eq(F_49(x), F_19(x) + F_214(x) + F_261(x) + F_50(x) + F_99(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_56(x))
Eq(F_52(x), F_40(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_44(x))
Eq(F_56(x), F_49(x) + F_57(x))
Eq(F_57(x), F_19(x) + F_212(x) + F_213(x) + F_58(x) + F_62(x) + F_63(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_61(x))
Eq(F_60(x), F_53(x))
Eq(F_61(x), F_57(x))
Eq(F_62(x), 0)
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), 3*F_19(x) + F_67(x) + F_80(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_72(x))
Eq(F_69(x), F_31(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_31(x)*F_4(x))
Eq(F_72(x), F_66(x) + F_73(x))
Eq(F_73(x), 3*F_19(x) + F_74(x) + F_78(x) + F_79(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_70(x))
Eq(F_77(x), F_73(x))
Eq(F_78(x), 0)
Eq(F_79(x), F_4(x)*F_66(x))
Eq(F_80(x), F_4(x)*F_81(x))
Eq(F_81(x), F_103(x) + 2*F_19(x) + F_82(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_86(x))
Eq(F_84(x), F_27(x) + F_85(x))
Eq(F_85(x), F_41(x))
Eq(F_86(x), F_81(x) + F_87(x))
Eq(F_87(x), F_102(x) + 2*F_19(x) + F_88(x) + F_99(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_92(x))
Eq(F_90(x), F_85(x) + F_91(x))
Eq(F_91(x), F_54(x))
Eq(F_92(x), F_87(x) + F_93(x))
Eq(F_93(x), 2*F_19(x) + F_62(x) + F_63(x) + F_94(x) + F_98(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_91(x))
Eq(F_97(x), F_93(x))
Eq(F_98(x), 0)
Eq(F_99(x), F_100(x)*F_4(x))
Eq(F_100(x), F_101(x) + F_65(x))
Eq(F_101(x), F_81(x))
Eq(F_102(x), 0)
Eq(F_103(x), F_104(x)*F_4(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x) + F_19(x) + F_211(x))
Eq(F_106(x), F_107(x)*F_4(x))
Eq(F_107(x), F_108(x) + F_120(x))
Eq(F_108(x), F_109(x) + F_4(x))
Eq(F_109(x), F_110(x) + F_114(x) + F_19(x))
Eq(F_110(x), F_111(x)*F_4(x))
Eq(F_111(x), F_112(x) + F_115(x))
Eq(F_112(x), F_113(x) + F_4(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), x**2)
Eq(F_115(x), F_116(x) + F_118(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), x**2)
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_113(x)*F_4(x))
Eq(F_120(x), F_105(x) + F_121(x))
Eq(F_121(x), F_122(x) + F_188(x) + F_19(x) + F_208(x))
Eq(F_122(x), F_123(x)*F_4(x))
Eq(F_123(x), F_124(x) + F_133(x))
Eq(F_124(x), F_109(x) + F_125(x))
Eq(F_125(x), F_126(x) + F_130(x) + F_132(x) + F_19(x))
Eq(F_126(x), F_127(x)*F_4(x))
Eq(F_127(x), F_128(x) + F_129(x))
Eq(F_128(x), F_113(x))
Eq(F_129(x), F_118(x))
Eq(F_130(x), F_131(x)*F_4(x))
Eq(F_131(x), F_115(x))
Eq(F_132(x), 0)
Eq(F_133(x), F_121(x) + F_134(x))
Eq(F_134(x), F_135(x) + F_184(x) + F_187(x) + F_19(x) + F_190(x))
Eq(F_135(x), F_136(x)*F_4(x))
Eq(F_136(x), F_137(x) + F_141(x))
Eq(F_137(x), F_125(x) + F_138(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_140(x)*F_4(x))
Eq(F_140(x), F_129(x))
Eq(F_141(x), F_134(x) + F_142(x))
Eq(F_142(x), F_143(x) + F_147(x) + F_148(x) + F_183(x) + F_189(x) + F_19(x))
Eq(F_143(x), F_144(x)*F_4(x))
Eq(F_144(x), F_145(x) + F_146(x))
Eq(F_145(x), F_138(x))
Eq(F_146(x), F_142(x))
Eq(F_147(x), 0)
Eq(F_148(x), F_149(x)*F_4(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_152(x) + F_165(x) + 3*F_19(x))
Eq(F_152(x), F_153(x)*F_4(x))
Eq(F_153(x), F_154(x) + F_157(x))
Eq(F_154(x), F_118(x) + F_155(x))
Eq(F_155(x), F_156(x))
Eq(F_156(x), F_118(x)*F_4(x))
Eq(F_157(x), F_151(x) + F_158(x))
Eq(F_158(x), F_159(x) + F_163(x) + F_164(x) + 3*F_19(x))
Eq(F_159(x), F_160(x)*F_4(x))
Eq(F_160(x), F_161(x) + F_162(x))
Eq(F_161(x), F_155(x))
Eq(F_162(x), F_158(x))
Eq(F_163(x), 0)
Eq(F_164(x), F_151(x)*F_4(x))
Eq(F_165(x), F_166(x)*F_4(x))
Eq(F_166(x), F_167(x) + F_188(x) + 2*F_19(x))
Eq(F_167(x), F_168(x)*F_4(x))
Eq(F_168(x), F_169(x) + F_171(x))
Eq(F_169(x), F_113(x) + F_170(x))
Eq(F_170(x), F_126(x))
Eq(F_171(x), F_166(x) + F_172(x))
Eq(F_172(x), F_173(x) + F_184(x) + F_187(x) + 2*F_19(x))
Eq(F_173(x), F_174(x)*F_4(x))
Eq(F_174(x), F_175(x) + F_177(x))
Eq(F_175(x), F_170(x) + F_176(x))
Eq(F_176(x), F_139(x))
Eq(F_177(x), F_172(x) + F_178(x))
Eq(F_178(x), F_147(x) + F_148(x) + F_179(x) + F_183(x) + 2*F_19(x))
Eq(F_179(x), F_180(x)*F_4(x))
Eq(F_180(x), F_181(x) + F_182(x))
Eq(F_181(x), F_176(x))
Eq(F_182(x), F_178(x))
Eq(F_183(x), 0)
Eq(F_184(x), F_185(x)*F_4(x))
Eq(F_185(x), F_150(x) + F_186(x))
Eq(F_186(x), F_166(x))
Eq(F_187(x), 0)
Eq(F_188(x), F_105(x)*F_4(x))
Eq(F_189(x), 0)
Eq(F_190(x), F_191(x)*F_4(x))
Eq(F_191(x), F_192(x))
Eq(F_192(x), F_151(x) + F_193(x))
Eq(F_193(x), 2*F_19(x) + F_194(x) + F_207(x))
Eq(F_194(x), F_195(x)*F_4(x))
Eq(F_195(x), F_196(x) + F_199(x))
Eq(F_196(x), F_116(x) + F_197(x))
Eq(F_197(x), F_198(x))
Eq(F_198(x), F_116(x)*F_4(x))
Eq(F_199(x), F_193(x) + F_200(x))
Eq(F_200(x), 2*F_19(x) + F_201(x) + F_205(x) + F_206(x))
Eq(F_201(x), F_202(x)*F_4(x))
Eq(F_202(x), F_203(x) + F_204(x))
Eq(F_203(x), F_197(x))
Eq(F_204(x), F_200(x))
Eq(F_205(x), 0)
Eq(F_206(x), F_193(x)*F_4(x))
Eq(F_207(x), F_105(x)*F_4(x))
Eq(F_208(x), F_209(x)*F_4(x))
Eq(F_209(x), F_192(x) + F_210(x))
Eq(F_210(x), F_105(x) + F_166(x))
Eq(F_211(x), F_2(x)*F_4(x))
Eq(F_212(x), 0)
Eq(F_213(x), 0)
Eq(F_214(x), F_215(x)*F_4(x))
Eq(F_215(x), F_216(x))
Eq(F_216(x), F_217(x) + F_66(x))
Eq(F_217(x), 2*F_19(x) + F_218(x) + F_231(x))
Eq(F_218(x), F_219(x)*F_4(x))
Eq(F_219(x), F_220(x) + F_223(x))
Eq(F_220(x), F_15(x) + F_221(x))
Eq(F_221(x), F_222(x))
Eq(F_222(x), F_15(x)*F_4(x))
Eq(F_223(x), F_217(x) + F_224(x))
Eq(F_224(x), 2*F_19(x) + F_225(x) + F_229(x) + F_230(x))
Eq(F_225(x), F_226(x)*F_4(x))
Eq(F_226(x), F_227(x) + F_228(x))
Eq(F_227(x), F_221(x))
Eq(F_228(x), F_224(x))
Eq(F_229(x), 0)
Eq(F_230(x), F_217(x)*F_4(x))
Eq(F_231(x), F_232(x)*F_4(x))
Eq(F_232(x), F_19(x) + F_233(x) + F_259(x))
Eq(F_233(x), F_234(x)*F_4(x))
Eq(F_234(x), F_235(x) + F_237(x))
Eq(F_235(x), F_11(x) + F_236(x))
Eq(F_236(x), F_19(x) + F_24(x) + F_28(x))
Eq(F_237(x), F_232(x) + F_238(x))
Eq(F_238(x), F_103(x) + F_19(x) + F_239(x) + F_256(x))
Eq(F_239(x), F_240(x)*F_4(x))
Eq(F_240(x), F_241(x) + F_244(x))
Eq(F_241(x), F_236(x) + F_242(x))
Eq(F_242(x), F_19(x) + F_243(x) + F_41(x) + F_45(x))
Eq(F_243(x), 0)
Eq(F_244(x), F_238(x) + F_245(x))
Eq(F_245(x), F_102(x) + F_19(x) + F_214(x) + F_246(x) + F_99(x))
Eq(F_246(x), F_247(x)*F_4(x))
Eq(F_247(x), F_248(x) + F_250(x))
Eq(F_248(x), F_242(x) + F_249(x))
Eq(F_249(x), F_54(x))
Eq(F_250(x), F_245(x) + F_251(x))
Eq(F_251(x), F_19(x) + F_212(x) + F_252(x) + F_62(x) + F_63(x) + F_98(x))
Eq(F_252(x), F_253(x)*F_4(x))
Eq(F_253(x), F_254(x) + F_255(x))
Eq(F_254(x), F_249(x))
Eq(F_255(x), F_251(x))
Eq(F_256(x), F_257(x)*F_4(x))
Eq(F_257(x), F_216(x) + F_258(x))
Eq(F_258(x), F_232(x) + F_81(x))
Eq(F_259(x), F_260(x)*F_4(x))
Eq(F_260(x), F_105(x) + F_2(x))
Eq(F_261(x), 0)
Eq(F_262(x), F_263(x)*F_4(x))
Eq(F_263(x), F_264(x))
Eq(F_264(x), F_105(x) + F_217(x))
Eq(F_265(x), F_266(x)*F_4(x))
Eq(F_266(x), F_264(x) + F_267(x))
Eq(F_267(x), F_2(x) + F_232(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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