0132_0213_1203_1230
Counting sequence:
1, 1, 2, 6, 20, 68, 233, 803, 2788, 9762, 34479, 122797, 440718, 1592781, 5792438, 21183150, 77855591, 287433789, 1065473298, 3964036000, 14797154681, 55403631964, 208020940198, 783046021569, 2954559800690, 11172413310260, 42333248529427, 160707215892066, 611157685747788, 2328014056464277, 8881520623791453, 33932634291990684, 129819245679099575, 497299241592241242, 1907315477466822558, 7323600483432579752, 28151255153500023916, 108322222194606555966, 417216568330213748918, 1608454889334877756766, 6206406810762530323210, 23968321815767331911976, 92636961841992329469206, 358314714629567375996572, 1386960358502428194909988, 5372406389097598271143890, 20824101211810214593431458, 80768917225509567010228248, 313466801092846473586972158, 1217299706624028787487677036, 4729902093060567590211707228, 18388487837014613939564861896, 71527032097797480981508570912, 278366067900118231194168676764, 1083867810674331089186872294796, 4222238196239805301390916479140, 16455397439578110854695336790244, 64160312083147446900397082432104, 250271016783067664758338416344388, 976640024137697658790327914550816, 3812698977505013522392673398135696, 14890147681405683146556098464755516, 58173968253017883226845797954506277, 227361290817714024161731032060183492, 888909812772596803125550234169356056, 3476543069299887402037523064454700572, 13601345497400897005343957813485651514, 53229976391879669144489737452157816447, 208385163630466427435886780461135203672, 816036504474872782295159451101361177930, 3196545998127904646875423299201695745263, 12524989543765402133848486564279490573604, 49090271530890024754550489722941614274378, 192456191764433688568822967402710839833383, 754716082451531640892527496052399572117022, 2960380796930577020179001802018166248994996, 11615045610761906833427465062936610493229669, 45582784194996759952857280107058001255281836, 178930629461417749915821820919842849217490386, 702538077840819135134392485259293048616801583, 2759013989379352461160175764162213842750391330, 10837632044622749978169481816805033063607993384, 42580333729066684928687732725175260201705091925, 167330710846044648509917682143677974531197854370, 657706359639961443950260728293610426077596836336, 2585688150275070484455566503751727494495605527507, 10167307697308938228582828568280964738539630746184, 39987069153705439053255122171714302828917678654852, 157295064950602780688974920101200609533054735662877, 618857602354638649181668534091585622231693483581030, 2435256584409099124182945654749895467261589805628848, 9584630915576732033194440112994732286041058226833159, 37729504017252408628197980858513089266610820967679088, 148545756017713673914460094366520179285485080907274128, 584939992903169974671152605279731037597627529660725147, 2303736534376370104497822457904015312696749850424265506, 9074512207302933719355671595242883026435559321583929884, 35750437084788381593399416453865297673067158918163157671, 140865828424147121670243107904862062773877353012697522376, 555130216292590347479822887601808945114393680095710750978, 2188002023073221053461708845319934055930848315183887749465
Generating function in Maple syntax:
1/2*((-x^5+2*x^4+3*x^3-6*x^2+4*x-1)*(1-4*x)^(1/2)+5*x^5-2*x^4-13*x^3+14*x^2-6*x+1)/x^2/(x^2+x-1)/(x-1)
Generating function in latex syntax:
\frac{\left(-x^{5}+2 x^{4}+3 x^{3}-6 x^{2}+4 x -1\right) \sqrt{1-4 x}+5 x^{5}-2 x^{4}-13 x^{3}+14 x^{2}-6 x +1}{2 x^{2} \left(x^{2}+x -1\right) \left(x -1\right)}
Generating function in sympy syntax:
(5*x**5/2 - x**4 - 13*x**3/2 + 7*x**2 - 3*x + sqrt(1 - 4*x)*(-x**5 + 2*x**4 + 3*x**3 - 6*x**2 + 4*x - 1)/2 + 1/2)/(x**2*(x - 1)*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
x^2*(x-1)^2*(x^2+x-1)^2*F(x)^2-(x-1)*(x^2+x-1)*(5*x^5-2*x^4-13*x^3+14*x^2-6*x+1)*F(x)+x^9+2*x^8-6*x^7-7*x^6+19*x^5+x^4-22*x^3+19*x^2-7*x+1 = 0
Implicit equation for the generating function in latex syntax:
x^{2} \left(x -1\right)^{2} \left(x^{2}+x -1\right)^{2} F \! \left(x \right)^{2}-\left(x -1\right) \left(x^{2}+x -1\right) \left(5 x^{5}-2 x^{4}-13 x^{3}+14 x^{2}-6 x +1\right) F \! \left(x \right)+x^{9}+2 x^{8}-6 x^{7}-7 x^{6}+19 x^{5}+x^{4}-22 x^{3}+19 x^{2}-7 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 68
a(6) = 233
a(7) = 803
a(8) = 2788
a(9) = 9762
a(n+9) = 2*(-1+2*n)/(11+n)*a(n)-2*(9*n+16)/(11+n)*a(2+n)-(9*n+13)/(11+n)*a(n+1)+(171+49*n)/(11+n)*a(n+3)-(11*n+103)/(11+n)*a(n+4)-8*(7*n+32)/(11+n)*a(n+5)+10*(7*n+46)/(11+n)*a(n+6)-2*(19*n+155)/(11+n)*a(n+7)+2*(5*n+48)/(11+n)*a(n+8), n >= 10
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 20
a \! \left(5\right) = 68
a \! \left(6\right) = 233
a \! \left(7\right) = 803
a \! \left(8\right) = 2788
a \! \left(9\right) = 9762
a \! \left(n +9\right) = \frac{2 \left(-1+2 n \right) a \! \left(n \right)}{11+n}-\frac{2 \left(9 n +16\right) a \! \left(2+n \right)}{11+n}-\frac{\left(9 n +13\right) a \! \left(n +1\right)}{11+n}+\frac{\left(171+49 n \right) a \! \left(n +3\right)}{11+n}-\frac{\left(11 n +103\right) a \! \left(n +4\right)}{11+n}-\frac{8 \left(7 n +32\right) a \! \left(n +5\right)}{11+n}+\frac{10 \left(7 n +46\right) a \! \left(n +6\right)}{11+n}-\frac{2 \left(19 n +155\right) a \! \left(n +7\right)}{11+n}+\frac{2 \left(5 n +48\right) a \! \left(n +8\right)}{11+n}, \quad n \geq 10
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21186/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[11,x]*F[3,x]
F[3,x] = F[1,x]+F[252,x]+F[4,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[7,x,k[0]]+F[9,x,k[0]]
F[7,x,k[0]] = F[6,x,k[0]]*F[8,x,k[0]]
F[8,x,k[0]] = k[0]*x
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[11,x] = x
F[12,x,k[0]] = F[11,x]*F[13,x,k[0]]
F[13,x,k[0]] = F[121,x,k[0]]+F[14,x]
F[14,x] = F[15,x]+F[52,x]
F[15,x] = F[16,x]+F[33,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[11,x]*F[19,x]
F[19,x] = F[20,x]+F[23,x]
F[20,x] = F[1,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[11,x]*F[20,x]
F[23,x] = F[24,x]+F[31,x]
F[24,x] = F[25,x]
F[25,x] = F[11,x]*F[26,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[1,x]+F[11,x]
F[28,x] = F[24,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[11,x]*F[24,x]
F[31,x] = F[32,x]
F[32,x] = F[11,x]*F[23,x]
F[33,x] = F[21,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[11,x]*F[36,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[11,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[11,x]*F[37,x]
F[40,x] = F[41,x]+F[50,x]
F[41,x] = F[42,x]
F[42,x] = F[11,x]*F[43,x]
F[43,x] = F[44,x]+F[47,x]
F[44,x] = F[11,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = x^2
F[47,x] = F[41,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[11,x]*F[41,x]
F[50,x] = F[51,x]
F[51,x] = F[11,x]*F[40,x]
F[52,x] = F[100,x]+F[53,x]
F[53,x] = F[54,x]+F[57,x]
F[54,x] = F[55,x]
F[55,x] = F[11,x]*F[56,x]
F[56,x] = F[1,x]+F[54,x]
F[57,x] = F[58,x]+F[59,x]+F[61,x]
F[58,x] = 0
F[59,x] = F[11,x]*F[60,x]
F[60,x] = F[17,x]+F[57,x]
F[61,x] = F[11,x]*F[62,x]
F[62,x] = F[63,x]+F[68,x]
F[63,x] = F[54,x]+F[64,x]
F[64,x] = F[58,x]+F[65,x]+F[67,x]
F[65,x] = F[11,x]*F[66,x]
F[66,x] = F[21,x]+F[64,x]
F[67,x] = F[11,x]*F[63,x]
F[68,x] = F[69,x]+F[90,x]
F[69,x] = F[58,x]+F[70,x]+F[75,x]
F[70,x] = F[11,x]*F[71,x]
F[71,x] = F[54,x]+F[72,x]
F[72,x] = F[58,x]+F[70,x]+F[73,x]
F[73,x] = F[11,x]*F[74,x]
F[74,x] = F[54,x]+F[72,x]
F[75,x] = F[11,x]*F[76,x]
F[76,x] = F[77,x]+F[82,x]
F[77,x] = F[54,x]+F[78,x]
F[78,x] = F[58,x]+F[79,x]+F[81,x]
F[79,x] = F[11,x]*F[80,x]
F[80,x] = F[11,x]+F[78,x]
F[81,x] = F[11,x]*F[54,x]
F[82,x] = F[69,x]+F[83,x]
F[83,x] = 2*F[58,x]+F[84,x]+F[89,x]
F[84,x] = F[11,x]*F[85,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[81,x]
F[87,x] = 2*F[58,x]+F[84,x]+F[88,x]
F[88,x] = F[11,x]*F[72,x]
F[89,x] = F[11,x]*F[69,x]
F[90,x] = 2*F[58,x]+F[91,x]+F[99,x]
F[91,x] = F[11,x]*F[92,x]
F[92,x] = F[93,x]+F[96,x]
F[93,x] = F[94,x]
F[94,x] = F[11,x]*F[95,x]
F[95,x] = F[54,x]+F[93,x]
F[96,x] = 2*F[58,x]+F[91,x]+F[97,x]
F[97,x] = F[11,x]*F[98,x]
F[98,x] = F[72,x]+F[96,x]
F[99,x] = F[11,x]*F[68,x]
F[100,x] = F[101,x]+F[64,x]
F[101,x] = 2*F[58,x]+F[102,x]+F[104,x]
F[102,x] = F[103,x]*F[11,x]
F[103,x] = F[101,x]+F[34,x]
F[104,x] = F[105,x]*F[11,x]
F[105,x] = F[106,x]+F[109,x]
F[106,x] = F[107,x]+F[86,x]
F[107,x] = F[108,x]
F[108,x] = F[106,x]*F[11,x]
F[109,x] = F[110,x]+F[119,x]
F[110,x] = F[111,x]
F[111,x] = F[11,x]*F[112,x]
F[112,x] = F[113,x]+F[116,x]
F[113,x] = F[114,x]+F[86,x]
F[114,x] = F[115,x]
F[115,x] = F[11,x]*F[86,x]
F[116,x] = F[110,x]+F[117,x]
F[117,x] = F[118,x]
F[118,x] = F[11,x]*F[110,x]
F[119,x] = F[120,x]
F[120,x] = F[109,x]*F[11,x]
F[121,x,k[0]] = F[122,x,k[0]]+F[187,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]+F[165,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]+F[127,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]
F[125,x,k[0]] = F[126,x,k[0]]*F[8,x,k[0]]
F[126,x,k[0]] = F[1,x]+F[124,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]+F[130,x,k[0]]+F[58,x]
F[128,x,k[0]] = F[129,x,k[0]]*F[8,x,k[0]]
F[129,x,k[0]] = F[127,x,k[0]]+F[17,x]
F[130,x,k[0]] = F[11,x]*F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]+F[137,x,k[0]]
F[132,x,k[0]] = F[124,x,k[0]]+F[133,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]+F[136,x,k[0]]+F[58,x]
F[134,x,k[0]] = F[135,x,k[0]]*F[8,x,k[0]]
F[135,x,k[0]] = F[133,x,k[0]]+F[21,x]
F[136,x,k[0]] = F[11,x]*F[132,x,k[0]]
F[137,x,k[0]] = F[138,x,k[0]]+F[158,x,k[0]]
F[138,x,k[0]] = F[139,x,k[0]]+F[144,x,k[0]]+F[58,x]
F[139,x,k[0]] = F[140,x,k[0]]*F[8,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]+F[54,x]
F[141,x,k[0]] = F[139,x,k[0]]+F[142,x,k[0]]+F[58,x]
F[142,x,k[0]] = F[11,x]*F[143,x,k[0]]
F[143,x,k[0]] = F[124,x,k[0]]+F[141,x,k[0]]
F[144,x,k[0]] = F[11,x]*F[145,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]+F[151,x,k[0]]
F[146,x,k[0]] = F[124,x,k[0]]+F[147,x,k[0]]
F[147,x,k[0]] = F[148,x,k[0]]+F[150,x,k[0]]+F[58,x]
F[148,x,k[0]] = F[149,x,k[0]]*F[8,x,k[0]]
F[149,x,k[0]] = F[11,x]+F[147,x,k[0]]
F[150,x,k[0]] = F[11,x]*F[124,x,k[0]]
F[151,x,k[0]] = F[138,x,k[0]]+F[152,x,k[0]]
F[152,x,k[0]] = 2*F[58,x]+F[153,x,k[0]]+F[157,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]*F[8,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]+F[86,x]
F[155,x,k[0]] = 2*F[58,x]+F[153,x,k[0]]+F[156,x,k[0]]
F[156,x,k[0]] = F[11,x]*F[141,x,k[0]]
F[157,x,k[0]] = F[11,x]*F[138,x,k[0]]
F[158,x,k[0]] = 2*F[58,x]+F[159,x,k[0]]+F[164,x,k[0]]
F[159,x,k[0]] = F[160,x,k[0]]*F[8,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]+F[93,x]
F[161,x,k[0]] = 2*F[58,x]+F[159,x,k[0]]+F[162,x,k[0]]
F[162,x,k[0]] = F[11,x]*F[163,x,k[0]]
F[163,x,k[0]] = F[141,x,k[0]]+F[161,x,k[0]]
F[164,x,k[0]] = F[11,x]*F[137,x,k[0]]
F[165,x,k[0]] = F[133,x,k[0]]+F[166,x,k[0]]
F[166,x,k[0]] = 2*F[58,x]+F[167,x,k[0]]+F[169,x,k[0]]
F[167,x,k[0]] = F[168,x,k[0]]*F[8,x,k[0]]
F[168,x,k[0]] = F[166,x,k[0]]+F[34,x]
F[169,x,k[0]] = F[11,x]*F[170,x,k[0]]
F[170,x,k[0]] = F[171,x,k[0]]+F[175,x,k[0]]
F[171,x,k[0]] = F[172,x,k[0]]+F[173,x,k[0]]
F[172,x,k[0]] = F[150,x,k[0]]
F[173,x,k[0]] = F[174,x,k[0]]
F[174,x,k[0]] = F[11,x]*F[171,x,k[0]]
F[175,x,k[0]] = F[176,x,k[0]]+F[185,x,k[0]]
F[176,x,k[0]] = F[177,x,k[0]]
F[177,x,k[0]] = F[11,x]*F[178,x,k[0]]
F[178,x,k[0]] = F[179,x,k[0]]+F[182,x,k[0]]
F[179,x,k[0]] = F[172,x,k[0]]+F[180,x,k[0]]
F[180,x,k[0]] = F[181,x,k[0]]
F[181,x,k[0]] = F[11,x]*F[172,x,k[0]]
F[182,x,k[0]] = F[176,x,k[0]]+F[183,x,k[0]]
F[183,x,k[0]] = F[184,x,k[0]]
F[184,x,k[0]] = F[11,x]*F[176,x,k[0]]
F[185,x,k[0]] = F[186,x,k[0]]
F[186,x,k[0]] = F[11,x]*F[175,x,k[0]]
F[187,x,k[0]] = F[188,x,k[0]]+F[230,x,k[0]]
F[188,x,k[0]] = F[189,x,k[0]]+F[192,x,k[0]]
F[189,x,k[0]] = F[190,x,k[0]]
F[190,x,k[0]] = F[11,x]*F[191,x,k[0]]
F[191,x,k[0]] = F[124,x,k[0]]+F[189,x,k[0]]
F[192,x,k[0]] = 2*F[58,x]+F[193,x,k[0]]+F[195,x,k[0]]
F[193,x,k[0]] = F[11,x]*F[194,x,k[0]]
F[194,x,k[0]] = F[127,x,k[0]]+F[192,x,k[0]]
F[195,x,k[0]] = F[11,x]*F[196,x,k[0]]
F[196,x,k[0]] = F[197,x,k[0]]+F[202,x,k[0]]
F[197,x,k[0]] = F[189,x,k[0]]+F[198,x,k[0]]
F[198,x,k[0]] = 2*F[58,x]+F[199,x,k[0]]+F[201,x,k[0]]
F[199,x,k[0]] = F[11,x]*F[200,x,k[0]]
F[200,x,k[0]] = F[133,x,k[0]]+F[198,x,k[0]]
F[201,x,k[0]] = F[11,x]*F[197,x,k[0]]
F[202,x,k[0]] = F[203,x,k[0]]+F[223,x,k[0]]
F[203,x,k[0]] = 2*F[58,x]+F[204,x,k[0]]+F[209,x,k[0]]
F[204,x,k[0]] = F[11,x]*F[205,x,k[0]]
F[205,x,k[0]] = F[141,x,k[0]]+F[206,x,k[0]]
F[206,x,k[0]] = 2*F[58,x]+F[204,x,k[0]]+F[207,x,k[0]]
F[207,x,k[0]] = F[11,x]*F[208,x,k[0]]
F[208,x,k[0]] = F[189,x,k[0]]+F[206,x,k[0]]
F[209,x,k[0]] = F[11,x]*F[210,x,k[0]]
F[210,x,k[0]] = F[211,x,k[0]]+F[216,x,k[0]]
F[211,x,k[0]] = F[189,x,k[0]]+F[212,x,k[0]]
F[212,x,k[0]] = 2*F[58,x]+F[213,x,k[0]]+F[215,x,k[0]]
F[213,x,k[0]] = F[11,x]*F[214,x,k[0]]
F[214,x,k[0]] = F[147,x,k[0]]+F[212,x,k[0]]
F[215,x,k[0]] = F[11,x]*F[189,x,k[0]]
F[216,x,k[0]] = F[203,x,k[0]]+F[217,x,k[0]]
F[217,x,k[0]] = 3*F[58,x]+F[218,x,k[0]]+F[222,x,k[0]]
F[218,x,k[0]] = F[11,x]*F[219,x,k[0]]
F[219,x,k[0]] = F[155,x,k[0]]+F[220,x,k[0]]
F[220,x,k[0]] = 3*F[58,x]+F[218,x,k[0]]+F[221,x,k[0]]
F[221,x,k[0]] = F[11,x]*F[206,x,k[0]]
F[222,x,k[0]] = F[11,x]*F[203,x,k[0]]
F[223,x,k[0]] = 3*F[58,x]+F[224,x,k[0]]+F[229,x,k[0]]
F[224,x,k[0]] = F[11,x]*F[225,x,k[0]]
F[225,x,k[0]] = F[161,x,k[0]]+F[226,x,k[0]]
F[226,x,k[0]] = 3*F[58,x]+F[224,x,k[0]]+F[227,x,k[0]]
F[227,x,k[0]] = F[11,x]*F[228,x,k[0]]
F[228,x,k[0]] = F[206,x,k[0]]+F[226,x,k[0]]
F[229,x,k[0]] = F[11,x]*F[202,x,k[0]]
F[230,x,k[0]] = F[198,x,k[0]]+F[231,x,k[0]]
F[231,x,k[0]] = 3*F[58,x]+F[232,x,k[0]]+F[234,x,k[0]]
F[232,x,k[0]] = F[11,x]*F[233,x,k[0]]
F[233,x,k[0]] = F[166,x,k[0]]+F[231,x,k[0]]
F[234,x,k[0]] = F[11,x]*F[235,x,k[0]]
F[235,x,k[0]] = F[236,x,k[0]]+F[240,x,k[0]]
F[236,x,k[0]] = F[237,x,k[0]]+F[238,x,k[0]]
F[237,x,k[0]] = F[215,x,k[0]]
F[238,x,k[0]] = F[239,x,k[0]]
F[239,x,k[0]] = F[11,x]*F[236,x,k[0]]
F[240,x,k[0]] = F[241,x,k[0]]+F[250,x,k[0]]
F[241,x,k[0]] = F[242,x,k[0]]
F[242,x,k[0]] = F[11,x]*F[243,x,k[0]]
F[243,x,k[0]] = F[244,x,k[0]]+F[247,x,k[0]]
F[244,x,k[0]] = F[237,x,k[0]]+F[245,x,k[0]]
F[245,x,k[0]] = F[246,x,k[0]]
F[246,x,k[0]] = F[11,x]*F[237,x,k[0]]
F[247,x,k[0]] = F[241,x,k[0]]+F[248,x,k[0]]
F[248,x,k[0]] = F[249,x,k[0]]
F[249,x,k[0]] = F[11,x]*F[241,x,k[0]]
F[250,x,k[0]] = F[251,x,k[0]]
F[251,x,k[0]] = F[11,x]*F[240,x,k[0]]
F[252,x] = F[11,x]*F[14,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_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{252}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{7}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = y x
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{10}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{52}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{33}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \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_{23}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right) F_{20}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{31}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{11}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{28}\! \left(x \right) = F_{24}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{24}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{33}\! \left(x \right) = F_{21}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{11}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{11}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{11}\! \left(x \right) F_{37}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{50}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{11}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{47}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = x^{2}
F_{47}\! \left(x \right) = F_{41}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{11}\! \left(x \right) F_{41}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{11}\! \left(x \right) F_{40}\! \left(x \right)
F_{52}\! \left(x \right) = F_{100}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{57}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{11}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{1}\! \left(x \right)+F_{54}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)+F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = 0
F_{59}\! \left(x \right) = F_{11}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{17}\! \left(x \right)+F_{57}\! \left(x \right)
F_{61}\! \left(x \right) = F_{11}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{68}\! \left(x \right)
F_{63}\! \left(x \right) = F_{54}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{58}\! \left(x \right)+F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{65}\! \left(x \right) = F_{11}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{21}\! \left(x \right)+F_{64}\! \left(x \right)
F_{67}\! \left(x \right) = F_{11}\! \left(x \right) F_{63}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{90}\! \left(x \right)
F_{69}\! \left(x \right) = F_{58}\! \left(x \right)+F_{70}\! \left(x \right)+F_{75}\! \left(x \right)
F_{70}\! \left(x \right) = F_{11}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{54}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{58}\! \left(x \right)+F_{70}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{11}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{54}\! \left(x \right)+F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{11}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{82}\! \left(x \right)
F_{77}\! \left(x \right) = F_{54}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{58}\! \left(x \right)+F_{79}\! \left(x \right)+F_{81}\! \left(x \right)
F_{79}\! \left(x \right) = F_{11}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{11}\! \left(x \right)+F_{78}\! \left(x \right)
F_{81}\! \left(x \right) = F_{11}\! \left(x \right) F_{54}\! \left(x \right)
F_{82}\! \left(x \right) = F_{69}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = 2 F_{58}\! \left(x \right)+F_{84}\! \left(x \right)+F_{89}\! \left(x \right)
F_{84}\! \left(x \right) = F_{11}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{81}\! \left(x \right)
F_{87}\! \left(x \right) = 2 F_{58}\! \left(x \right)+F_{84}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{11}\! \left(x \right) F_{72}\! \left(x \right)
F_{89}\! \left(x \right) = F_{11}\! \left(x \right) F_{69}\! \left(x \right)
F_{90}\! \left(x \right) = 2 F_{58}\! \left(x \right)+F_{91}\! \left(x \right)+F_{99}\! \left(x \right)
F_{91}\! \left(x \right) = F_{11}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{96}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{11}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{54}\! \left(x \right)+F_{93}\! \left(x \right)
F_{96}\! \left(x \right) = 2 F_{58}\! \left(x \right)+F_{91}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{11}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{72}\! \left(x \right)+F_{96}\! \left(x \right)
F_{99}\! \left(x \right) = F_{11}\! \left(x \right) F_{68}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{64}\! \left(x \right)
F_{101}\! \left(x \right) = 2 F_{58}\! \left(x \right)+F_{102}\! \left(x \right)+F_{104}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{11}\! \left(x \right)
F_{103}\! \left(x \right) = F_{101}\! \left(x \right)+F_{34}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{11}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{109}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{86}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{106}\! \left(x \right) F_{11}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{119}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{11}\! \left(x \right) F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{116}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{86}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{11}\! \left(x \right) F_{86}\! \left(x \right)
F_{116}\! \left(x \right) = F_{110}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{11}\! \left(x \right) F_{110}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{109}\! \left(x \right) F_{11}\! \left(x \right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{187}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{165}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{124}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{130}\! \left(x , y\right)+F_{58}\! \left(x \right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{17}\! \left(x \right)
F_{130}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right)+F_{137}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{136}\! \left(x , y\right)+F_{58}\! \left(x \right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{21}\! \left(x \right)
F_{136}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{132}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{158}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right)+F_{144}\! \left(x , y\right)+F_{58}\! \left(x \right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{54}\! \left(x \right)
F_{141}\! \left(x , y\right) = F_{139}\! \left(x , y\right)+F_{142}\! \left(x , y\right)+F_{58}\! \left(x \right)
F_{142}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{143}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)+F_{151}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)+F_{150}\! \left(x , y\right)+F_{58}\! \left(x \right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{147}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{124}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = 2 F_{58}\! \left(x \right)+F_{153}\! \left(x , y\right)+F_{157}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right)+F_{86}\! \left(x \right)
F_{155}\! \left(x , y\right) = 2 F_{58}\! \left(x \right)+F_{153}\! \left(x , y\right)+F_{156}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{141}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{138}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = 2 F_{58}\! \left(x \right)+F_{159}\! \left(x , y\right)+F_{164}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{160}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{93}\! \left(x \right)
F_{161}\! \left(x , y\right) = 2 F_{58}\! \left(x \right)+F_{159}\! \left(x , y\right)+F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{161}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{137}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{166}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = 2 F_{58}\! \left(x \right)+F_{167}\! \left(x , y\right)+F_{169}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{34}\! \left(x \right)
F_{169}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{170}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right)+F_{175}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right)+F_{173}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{150}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{171}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{185}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right)+F_{182}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{172}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{172}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{183}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{176}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{186}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{175}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{188}\! \left(x , y\right)+F_{230}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{192}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{190}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{191}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{189}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = 2 F_{58}\! \left(x \right)+F_{193}\! \left(x , y\right)+F_{195}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{194}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{192}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{196}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right)+F_{202}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{198}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = 2 F_{58}\! \left(x \right)+F_{199}\! \left(x , y\right)+F_{201}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{200}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{198}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{197}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{223}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = 2 F_{58}\! \left(x \right)+F_{204}\! \left(x , y\right)+F_{209}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{205}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{206}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = 2 F_{58}\! \left(x \right)+F_{204}\! \left(x , y\right)+F_{207}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{208}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{206}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{210}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{211}\! \left(x , y\right)+F_{216}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{212}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = 2 F_{58}\! \left(x \right)+F_{213}\! \left(x , y\right)+F_{215}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{214}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{212}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{189}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{217}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = 3 F_{58}\! \left(x \right)+F_{218}\! \left(x , y\right)+F_{222}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{219}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{155}\! \left(x , y\right)+F_{220}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = 3 F_{58}\! \left(x \right)+F_{218}\! \left(x , y\right)+F_{221}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{206}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{203}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = 3 F_{58}\! \left(x \right)+F_{224}\! \left(x , y\right)+F_{229}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{225}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{226}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = 3 F_{58}\! \left(x \right)+F_{224}\! \left(x , y\right)+F_{227}\! \left(x , y\right)
F_{227}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{228}\! \left(x , y\right)
F_{228}\! \left(x , y\right) = F_{206}\! \left(x , y\right)+F_{226}\! \left(x , y\right)
F_{229}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{202}\! \left(x , y\right)
F_{230}\! \left(x , y\right) = F_{198}\! \left(x , y\right)+F_{231}\! \left(x , y\right)
F_{231}\! \left(x , y\right) = 3 F_{58}\! \left(x \right)+F_{232}\! \left(x , y\right)+F_{234}\! \left(x , y\right)
F_{232}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{233}\! \left(x , y\right)
F_{233}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{231}\! \left(x , y\right)
F_{234}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{235}\! \left(x , y\right)
F_{235}\! \left(x , y\right) = F_{236}\! \left(x , y\right)+F_{240}\! \left(x , y\right)
F_{236}\! \left(x , y\right) = F_{237}\! \left(x , y\right)+F_{238}\! \left(x , y\right)
F_{237}\! \left(x , y\right) = F_{215}\! \left(x , y\right)
F_{238}\! \left(x , y\right) = F_{239}\! \left(x , y\right)
F_{239}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{236}\! \left(x , y\right)
F_{240}\! \left(x , y\right) = F_{241}\! \left(x , y\right)+F_{250}\! \left(x , y\right)
F_{241}\! \left(x , y\right) = F_{242}\! \left(x , y\right)
F_{242}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{243}\! \left(x , y\right)
F_{243}\! \left(x , y\right) = F_{244}\! \left(x , y\right)+F_{247}\! \left(x , y\right)
F_{244}\! \left(x , y\right) = F_{237}\! \left(x , y\right)+F_{245}\! \left(x , y\right)
F_{245}\! \left(x , y\right) = F_{246}\! \left(x , y\right)
F_{246}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{237}\! \left(x , y\right)
F_{247}\! \left(x , y\right) = F_{241}\! \left(x , y\right)+F_{248}\! \left(x , y\right)
F_{248}\! \left(x , y\right) = F_{249}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{241}\! \left(x , y\right)
F_{250}\! \left(x , y\right) = F_{251}\! \left(x , y\right)
F_{251}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{240}\! \left(x , y\right)
F_{252}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \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_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_252(x) + F_4(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_12(x, k_0) + F_7(x, k_0) + F_9(x, k_0))
Eq(F_7(x, k_0), F_6(x, k_0)*F_8(x, k_0))
Eq(F_8(x, k_0), k_0*x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x))
Eq(F_10(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_11(x)*F_13(x, k_0))
Eq(F_13(x, k_0), F_121(x, k_0) + F_14(x))
Eq(F_14(x), F_15(x) + F_52(x))
Eq(F_15(x), F_16(x) + F_33(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_11(x)*F_19(x))
Eq(F_19(x), F_20(x) + F_23(x))
Eq(F_20(x), F_1(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_11(x)*F_20(x))
Eq(F_23(x), F_24(x) + F_31(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_11(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_1(x) + F_11(x))
Eq(F_28(x), F_24(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_11(x)*F_24(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_11(x)*F_23(x))
Eq(F_33(x), F_21(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_11(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_11(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_11(x)*F_37(x))
Eq(F_40(x), F_41(x) + F_50(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_11(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_47(x))
Eq(F_44(x), F_11(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), x**2)
Eq(F_47(x), F_41(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_11(x)*F_41(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_11(x)*F_40(x))
Eq(F_52(x), F_100(x) + F_53(x))
Eq(F_53(x), F_54(x) + F_57(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_11(x)*F_56(x))
Eq(F_56(x), F_1(x) + F_54(x))
Eq(F_57(x), F_58(x) + F_59(x) + F_61(x))
Eq(F_58(x), 0)
Eq(F_59(x), F_11(x)*F_60(x))
Eq(F_60(x), F_17(x) + F_57(x))
Eq(F_61(x), F_11(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_68(x))
Eq(F_63(x), F_54(x) + F_64(x))
Eq(F_64(x), F_58(x) + F_65(x) + F_67(x))
Eq(F_65(x), F_11(x)*F_66(x))
Eq(F_66(x), F_21(x) + F_64(x))
Eq(F_67(x), F_11(x)*F_63(x))
Eq(F_68(x), F_69(x) + F_90(x))
Eq(F_69(x), F_58(x) + F_70(x) + F_75(x))
Eq(F_70(x), F_11(x)*F_71(x))
Eq(F_71(x), F_54(x) + F_72(x))
Eq(F_72(x), F_58(x) + F_70(x) + F_73(x))
Eq(F_73(x), F_11(x)*F_74(x))
Eq(F_74(x), F_54(x) + F_72(x))
Eq(F_75(x), F_11(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_82(x))
Eq(F_77(x), F_54(x) + F_78(x))
Eq(F_78(x), F_58(x) + F_79(x) + F_81(x))
Eq(F_79(x), F_11(x)*F_80(x))
Eq(F_80(x), F_11(x) + F_78(x))
Eq(F_81(x), F_11(x)*F_54(x))
Eq(F_82(x), F_69(x) + F_83(x))
Eq(F_83(x), 2*F_58(x) + F_84(x) + F_89(x))
Eq(F_84(x), F_11(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_81(x))
Eq(F_87(x), 2*F_58(x) + F_84(x) + F_88(x))
Eq(F_88(x), F_11(x)*F_72(x))
Eq(F_89(x), F_11(x)*F_69(x))
Eq(F_90(x), 2*F_58(x) + F_91(x) + F_99(x))
Eq(F_91(x), F_11(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_96(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_11(x)*F_95(x))
Eq(F_95(x), F_54(x) + F_93(x))
Eq(F_96(x), 2*F_58(x) + F_91(x) + F_97(x))
Eq(F_97(x), F_11(x)*F_98(x))
Eq(F_98(x), F_72(x) + F_96(x))
Eq(F_99(x), F_11(x)*F_68(x))
Eq(F_100(x), F_101(x) + F_64(x))
Eq(F_101(x), F_102(x) + F_104(x) + 2*F_58(x))
Eq(F_102(x), F_103(x)*F_11(x))
Eq(F_103(x), F_101(x) + F_34(x))
Eq(F_104(x), F_105(x)*F_11(x))
Eq(F_105(x), F_106(x) + F_109(x))
Eq(F_106(x), F_107(x) + F_86(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_106(x)*F_11(x))
Eq(F_109(x), F_110(x) + F_119(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_11(x)*F_112(x))
Eq(F_112(x), F_113(x) + F_116(x))
Eq(F_113(x), F_114(x) + F_86(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_11(x)*F_86(x))
Eq(F_116(x), F_110(x) + F_117(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_11(x)*F_110(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_109(x)*F_11(x))
Eq(F_121(x, k_0), F_122(x, k_0) + F_187(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0) + F_165(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0) + F_127(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0)*F_8(x, k_0))
Eq(F_126(x, k_0), F_1(x) + F_124(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0) + F_130(x, k_0) + F_58(x))
Eq(F_128(x, k_0), F_129(x, k_0)*F_8(x, k_0))
Eq(F_129(x, k_0), F_127(x, k_0) + F_17(x))
Eq(F_130(x, k_0), F_11(x)*F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0) + F_137(x, k_0))
Eq(F_132(x, k_0), F_124(x, k_0) + F_133(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0) + F_136(x, k_0) + F_58(x))
Eq(F_134(x, k_0), F_135(x, k_0)*F_8(x, k_0))
Eq(F_135(x, k_0), F_133(x, k_0) + F_21(x))
Eq(F_136(x, k_0), F_11(x)*F_132(x, k_0))
Eq(F_137(x, k_0), F_138(x, k_0) + F_158(x, k_0))
Eq(F_138(x, k_0), F_139(x, k_0) + F_144(x, k_0) + F_58(x))
Eq(F_139(x, k_0), F_140(x, k_0)*F_8(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0) + F_54(x))
Eq(F_141(x, k_0), F_139(x, k_0) + F_142(x, k_0) + F_58(x))
Eq(F_142(x, k_0), F_11(x)*F_143(x, k_0))
Eq(F_143(x, k_0), F_124(x, k_0) + F_141(x, k_0))
Eq(F_144(x, k_0), F_11(x)*F_145(x, k_0))
Eq(F_145(x, k_0), F_146(x, k_0) + F_151(x, k_0))
Eq(F_146(x, k_0), F_124(x, k_0) + F_147(x, k_0))
Eq(F_147(x, k_0), F_148(x, k_0) + F_150(x, k_0) + F_58(x))
Eq(F_148(x, k_0), F_149(x, k_0)*F_8(x, k_0))
Eq(F_149(x, k_0), F_11(x) + F_147(x, k_0))
Eq(F_150(x, k_0), F_11(x)*F_124(x, k_0))
Eq(F_151(x, k_0), F_138(x, k_0) + F_152(x, k_0))
Eq(F_152(x, k_0), F_153(x, k_0) + F_157(x, k_0) + 2*F_58(x))
Eq(F_153(x, k_0), F_154(x, k_0)*F_8(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0) + F_86(x))
Eq(F_155(x, k_0), F_153(x, k_0) + F_156(x, k_0) + 2*F_58(x))
Eq(F_156(x, k_0), F_11(x)*F_141(x, k_0))
Eq(F_157(x, k_0), F_11(x)*F_138(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0) + F_164(x, k_0) + 2*F_58(x))
Eq(F_159(x, k_0), F_160(x, k_0)*F_8(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0) + F_93(x))
Eq(F_161(x, k_0), F_159(x, k_0) + F_162(x, k_0) + 2*F_58(x))
Eq(F_162(x, k_0), F_11(x)*F_163(x, k_0))
Eq(F_163(x, k_0), F_141(x, k_0) + F_161(x, k_0))
Eq(F_164(x, k_0), F_11(x)*F_137(x, k_0))
Eq(F_165(x, k_0), F_133(x, k_0) + F_166(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0) + F_169(x, k_0) + 2*F_58(x))
Eq(F_167(x, k_0), F_168(x, k_0)*F_8(x, k_0))
Eq(F_168(x, k_0), F_166(x, k_0) + F_34(x))
Eq(F_169(x, k_0), F_11(x)*F_170(x, k_0))
Eq(F_170(x, k_0), F_171(x, k_0) + F_175(x, k_0))
Eq(F_171(x, k_0), F_172(x, k_0) + F_173(x, k_0))
Eq(F_172(x, k_0), F_150(x, k_0))
Eq(F_173(x, k_0), F_174(x, k_0))
Eq(F_174(x, k_0), F_11(x)*F_171(x, k_0))
Eq(F_175(x, k_0), F_176(x, k_0) + F_185(x, k_0))
Eq(F_176(x, k_0), F_177(x, k_0))
Eq(F_177(x, k_0), F_11(x)*F_178(x, k_0))
Eq(F_178(x, k_0), F_179(x, k_0) + F_182(x, k_0))
Eq(F_179(x, k_0), F_172(x, k_0) + F_180(x, k_0))
Eq(F_180(x, k_0), F_181(x, k_0))
Eq(F_181(x, k_0), F_11(x)*F_172(x, k_0))
Eq(F_182(x, k_0), F_176(x, k_0) + F_183(x, k_0))
Eq(F_183(x, k_0), F_184(x, k_0))
Eq(F_184(x, k_0), F_11(x)*F_176(x, k_0))
Eq(F_185(x, k_0), F_186(x, k_0))
Eq(F_186(x, k_0), F_11(x)*F_175(x, k_0))
Eq(F_187(x, k_0), F_188(x, k_0) + F_230(x, k_0))
Eq(F_188(x, k_0), F_189(x, k_0) + F_192(x, k_0))
Eq(F_189(x, k_0), F_190(x, k_0))
Eq(F_190(x, k_0), F_11(x)*F_191(x, k_0))
Eq(F_191(x, k_0), F_124(x, k_0) + F_189(x, k_0))
Eq(F_192(x, k_0), F_193(x, k_0) + F_195(x, k_0) + 2*F_58(x))
Eq(F_193(x, k_0), F_11(x)*F_194(x, k_0))
Eq(F_194(x, k_0), F_127(x, k_0) + F_192(x, k_0))
Eq(F_195(x, k_0), F_11(x)*F_196(x, k_0))
Eq(F_196(x, k_0), F_197(x, k_0) + F_202(x, k_0))
Eq(F_197(x, k_0), F_189(x, k_0) + F_198(x, k_0))
Eq(F_198(x, k_0), F_199(x, k_0) + F_201(x, k_0) + 2*F_58(x))
Eq(F_199(x, k_0), F_11(x)*F_200(x, k_0))
Eq(F_200(x, k_0), F_133(x, k_0) + F_198(x, k_0))
Eq(F_201(x, k_0), F_11(x)*F_197(x, k_0))
Eq(F_202(x, k_0), F_203(x, k_0) + F_223(x, k_0))
Eq(F_203(x, k_0), F_204(x, k_0) + F_209(x, k_0) + 2*F_58(x))
Eq(F_204(x, k_0), F_11(x)*F_205(x, k_0))
Eq(F_205(x, k_0), F_141(x, k_0) + F_206(x, k_0))
Eq(F_206(x, k_0), F_204(x, k_0) + F_207(x, k_0) + 2*F_58(x))
Eq(F_207(x, k_0), F_11(x)*F_208(x, k_0))
Eq(F_208(x, k_0), F_189(x, k_0) + F_206(x, k_0))
Eq(F_209(x, k_0), F_11(x)*F_210(x, k_0))
Eq(F_210(x, k_0), F_211(x, k_0) + F_216(x, k_0))
Eq(F_211(x, k_0), F_189(x, k_0) + F_212(x, k_0))
Eq(F_212(x, k_0), F_213(x, k_0) + F_215(x, k_0) + 2*F_58(x))
Eq(F_213(x, k_0), F_11(x)*F_214(x, k_0))
Eq(F_214(x, k_0), F_147(x, k_0) + F_212(x, k_0))
Eq(F_215(x, k_0), F_11(x)*F_189(x, k_0))
Eq(F_216(x, k_0), F_203(x, k_0) + F_217(x, k_0))
Eq(F_217(x, k_0), F_218(x, k_0) + F_222(x, k_0) + 3*F_58(x))
Eq(F_218(x, k_0), F_11(x)*F_219(x, k_0))
Eq(F_219(x, k_0), F_155(x, k_0) + F_220(x, k_0))
Eq(F_220(x, k_0), F_218(x, k_0) + F_221(x, k_0) + 3*F_58(x))
Eq(F_221(x, k_0), F_11(x)*F_206(x, k_0))
Eq(F_222(x, k_0), F_11(x)*F_203(x, k_0))
Eq(F_223(x, k_0), F_224(x, k_0) + F_229(x, k_0) + 3*F_58(x))
Eq(F_224(x, k_0), F_11(x)*F_225(x, k_0))
Eq(F_225(x, k_0), F_161(x, k_0) + F_226(x, k_0))
Eq(F_226(x, k_0), F_224(x, k_0) + F_227(x, k_0) + 3*F_58(x))
Eq(F_227(x, k_0), F_11(x)*F_228(x, k_0))
Eq(F_228(x, k_0), F_206(x, k_0) + F_226(x, k_0))
Eq(F_229(x, k_0), F_11(x)*F_202(x, k_0))
Eq(F_230(x, k_0), F_198(x, k_0) + F_231(x, k_0))
Eq(F_231(x, k_0), F_232(x, k_0) + F_234(x, k_0) + 3*F_58(x))
Eq(F_232(x, k_0), F_11(x)*F_233(x, k_0))
Eq(F_233(x, k_0), F_166(x, k_0) + F_231(x, k_0))
Eq(F_234(x, k_0), F_11(x)*F_235(x, k_0))
Eq(F_235(x, k_0), F_236(x, k_0) + F_240(x, k_0))
Eq(F_236(x, k_0), F_237(x, k_0) + F_238(x, k_0))
Eq(F_237(x, k_0), F_215(x, k_0))
Eq(F_238(x, k_0), F_239(x, k_0))
Eq(F_239(x, k_0), F_11(x)*F_236(x, k_0))
Eq(F_240(x, k_0), F_241(x, k_0) + F_250(x, k_0))
Eq(F_241(x, k_0), F_242(x, k_0))
Eq(F_242(x, k_0), F_11(x)*F_243(x, k_0))
Eq(F_243(x, k_0), F_244(x, k_0) + F_247(x, k_0))
Eq(F_244(x, k_0), F_237(x, k_0) + F_245(x, k_0))
Eq(F_245(x, k_0), F_246(x, k_0))
Eq(F_246(x, k_0), F_11(x)*F_237(x, k_0))
Eq(F_247(x, k_0), F_241(x, k_0) + F_248(x, k_0))
Eq(F_248(x, k_0), F_249(x, k_0))
Eq(F_249(x, k_0), F_11(x)*F_241(x, k_0))
Eq(F_250(x, k_0), F_251(x, k_0))
Eq(F_251(x, k_0), F_11(x)*F_240(x, k_0))
Eq(F_252(x), F_11(x)*F_14(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.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion", "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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 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], "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, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "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, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "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": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0], [3, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": 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