0132_0213_3120
Counting sequence:
1, 1, 2, 6, 21, 73, 238, 721, 2044, 5492, 14178, 35610, 87938, 215295, 525787, 1286294, 3160692, 7812235, 19435271, 48669058, 122640467, 310825886, 791852703, 2026485203, 5206520173, 13421671869, 34697109772, 89909564367, 233436502611, 607059621989, 1580760867164, 4120657531699, 10750874889814, 28068880179292, 73324763302584, 191633745726020, 501013824054596, 1310243779054551, 3427312317622553, 8966728174785480, 23462632984284318, 61400073874081315, 160694157899102989, 420593064468162220, 1100901417021560005, 2881734054058481030, 7543526688909313581, 19747258317810103173, 51694993710022210823, 135331055373651744741, 354284520874453369090, 927494570858143343513, 2428142052279558323925, 6356814773865028508509, 16642063578535083442586, 43568888447080337824261, 114063606467188028592800, 298619899831051516144052, 781791949714309012005630, 2046747500558974202091182, 5358433330197638110094134, 14028517397985643183861119, 36727047382626005283678535, 96152479193552415453211482, 251730093897204556443603192, 659037199520114343743298731, 1725380277954657572258995715, 4517101139421722402877129814, 11825918067455889365198890855, 30960642751216008487915996798, 81055989230690868363205801131, 212207282365771274478623200727, 555565771388286737520699482321, 1454489856186085356366790434621, 3807903440631299874919522836968, 9969219742005150768616515884067, 26099754316728176258468015257479, 68330040228366127316038818773413, 178890360323741107616499733540552, 468341028483593806003858299494839, 1226132700268503144569259356536090, 3210057021924820522519062326324348, 8404038263351726665551758291454516, 22002057561101812865130961939184664, 57602134000456452523564799061757784, 150804343590392693516479120154878647, 394810895049211260894640610884533349, 1033628338070699025398852166410851340, 2706074112102759028752481501293546882, 7084593983943239169735216968399556835, 18547707810790110062157405470178511337, 48558529389857052908047445177352798016, 127127880240248289900409768730965445177, 332825111091036934181639432743761188678, 871347452547590017244639461728979066905, 2281217245570046666398972394436428319113, 5972304282176894158938527760629451092683, 15635695596944758322974837275665528370309, 40934782500536494152273889463014199426494, 107168651888244687452765547147099296979501, 280571173131000968112545994526571806496361
Generating function in Maple syntax:
(x^13-7*x^12+9*x^11+62*x^10-325*x^9+822*x^8-1378*x^7+1620*x^6-1352*x^5+799*x^4-327*x^3+88*x^2-14*x+1)/(x^2-3*x+1)/(2*x-1)^2/(-1+x)^8
Generating function in latex syntax:
\frac{x^{13}-7 x^{12}+9 x^{11}+62 x^{10}-325 x^{9}+822 x^{8}-1378 x^{7}+1620 x^{6}-1352 x^{5}+799 x^{4}-327 x^{3}+88 x^{2}-14 x +1}{\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} \left(-1+x \right)^{8}}
Generating function in sympy syntax:
(x**13 - 7*x**12 + 9*x**11 + 62*x**10 - 325*x**9 + 822*x**8 - 1378*x**7 + 1620*x**6 - 1352*x**5 + 799*x**4 - 327*x**3 + 88*x**2 - 14*x + 1)/((x - 1)**8*(2*x - 1)**2*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
-(x^2-3*x+1)*(2*x-1)^2*(-1+x)^8*F(x)+x^13-7*x^12+9*x^11+62*x^10-325*x^9+822*x^8-1378*x^7+1620*x^6-1352*x^5+799*x^4-327*x^3+88*x^2-14*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} \left(-1+x \right)^{8} F \! \left(x \right)+x^{13}-7 x^{12}+9 x^{11}+62 x^{10}-325 x^{9}+822 x^{8}-1378 x^{7}+1620 x^{6}-1352 x^{5}+799 x^{4}-327 x^{3}+88 x^{2}-14 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/5040*n^7-1/720*n^6-11/720*n^5+7/144*n^4-31/90*n^3+9/8*2^n*n-17/360*n^2+3-13/4*2^n+571/420*n-1/5*(3/2+1/2*5^(1/2))^(-n)*5^(1/2)+1/5*(3/2-1/2*5^(1/2))^(-n)*5^(1/2))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{n^{7}}{5040}-\frac{n^{6}}{720}-\frac{11 n^{5}}{720}+\frac{7 n^{4}}{144}-\frac{31 n^{3}}{90}+\frac{9 \,2^{n} n}{8}-\frac{17 n^{2}}{360}+3-\frac{13 \,2^{n}}{4}+\frac{571 n}{420}\\-\frac{\left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}}{5}+\frac{\left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}}{5} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 73
a(6) = 238
a(7) = 721
a(8) = 2044
a(9) = 5492
a(10) = 14178
a(11) = 35610
a(12) = 87938
a(13) = 215295
a(n+4) = -4*a(n)+16*a(n+1)-17*a(n+2)+7*a(n+3)-1/5040*n*(n^6-14*n^5-140*n^4+1330*n^3+2359*n^2-8876*n+10380), n >= 14
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 21
a \! \left(5\right) = 73
a \! \left(6\right) = 238
a \! \left(7\right) = 721
a \! \left(8\right) = 2044
a \! \left(9\right) = 5492
a \! \left(10\right) = 14178
a \! \left(11\right) = 35610
a \! \left(12\right) = 87938
a \! \left(13\right) = 215295
a \! \left(n +4\right) = -4 a \! \left(n \right)+16 a \! \left(n +1\right)-17 a \! \left(n +2\right)+7 a \! \left(n +3\right)-\frac{n \left(n^{6}-14 n^{5}-140 n^{4}+1330 n^{3}+2359 n^{2}-8876 n +10380\right)}{5040}, \quad n \geq 14
Specification 1
Strategy pack name: row_placements
Tree: http://permpal.com/tree/260/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[19,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[94,x]
F[4,x] = F[19,x]*F[5,x]
F[5,x] = F[1,x]+F[6,x]+F[60,x]+F[61,x]
F[6,x] = F[19,x]*F[7,x]
F[7,x] = F[1,x]+F[51,x]+F[52,x]+F[54,x]+F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[19,x]*F[29,x]
F[10,x] = F[1,x]+F[11,x]+F[8,x]
F[11,x] = F[12,x]*F[19,x]
F[12,x] = F[1,x]+F[11,x]+F[13,x]+F[42,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[19,x]*F[29,x]
F[15,x] = F[16,x]+F[20,x]+F[41,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[16,x]*F[19,x]
F[19,x] = x
F[20,x] = F[21,x]
F[21,x] = F[19,x]*F[22,x]
F[22,x] = F[15,x]+F[23,x]
F[23,x] = F[19,x]*F[24,x]*F[29,x]
F[24,x] = F[1,x]+F[25,x]+F[33,x]
F[25,x] = F[19,x]*F[26,x]
F[26,x] = 2*F[32,x]+F[1,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[19,x]*F[24,x]*F[29,x]
F[29,x] = F[1,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[19,x]*F[29,x]
F[32,x] = F[19,x]*F[26,x]
F[33,x] = F[19,x]*F[34,x]
F[34,x] = F[29,x]+F[35,x]
F[35,x] = F[17,x]+F[36,x]
F[36,x] = F[37,x]+F[38,x]+F[40,x]
F[37,x] = 0
F[38,x] = F[19,x]*F[39,x]
F[39,x] = F[30,x]+F[36,x]
F[40,x] = F[19,x]*F[35,x]
F[41,x] = F[15,x]*F[19,x]
F[42,x] = F[19,x]*F[43,x]
F[43,x] = F[1,x]+F[42,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[19,x]*F[29,x]*F[46,x]
F[46,x] = F[47,x]+F[50,x]
F[47,x] = F[1,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[19,x]*F[29,x]*F[47,x]
F[50,x] = F[16,x]*F[17,x]
F[51,x] = F[19,x]*F[7,x]
F[52,x] = F[53,x]
F[53,x] = F[19,x]*F[34,x]*F[47,x]
F[54,x] = F[19,x]*F[55,x]
F[55,x] = F[1,x]+F[13,x]+F[32,x]+F[54,x]+F[56,x]+F[58,x]
F[56,x] = F[57,x]
F[57,x] = F[16,x]*F[19,x]*F[47,x]
F[58,x] = F[19,x]*F[59,x]
F[59,x] = 2*F[56,x]+F[1,x]+F[44,x]+F[58,x]
F[60,x] = F[19,x]*F[5,x]
F[61,x] = F[19,x]*F[62,x]
F[62,x] = F[63,x]+F[69,x]
F[63,x] = F[64,x]+F[68,x]
F[64,x] = F[1,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[16,x]*F[19,x]*F[29,x]
F[68,x] = F[30,x]
F[69,x] = F[70,x]+F[93,x]
F[70,x] = F[17,x]+F[71,x]
F[71,x] = F[37,x]+F[72,x]+F[74,x]
F[72,x] = F[19,x]*F[73,x]
F[73,x] = F[65,x]+F[71,x]
F[74,x] = F[19,x]*F[75,x]
F[75,x] = F[35,x]+F[76,x]
F[76,x] = F[77,x]+F[83,x]
F[77,x] = F[37,x]+F[78,x]+F[81,x]
F[78,x] = F[19,x]*F[79,x]
F[79,x] = F[17,x]+F[80,x]
F[80,x] = F[78,x]
F[81,x] = F[19,x]*F[82,x]
F[82,x] = F[17,x]+F[77,x]
F[83,x] = 2*F[37,x]+F[84,x]+F[92,x]
F[84,x] = F[19,x]*F[85,x]
F[85,x] = F[86,x]+F[89,x]
F[86,x] = F[87,x]
F[87,x] = F[19,x]*F[88,x]
F[88,x] = F[17,x]+F[86,x]
F[89,x] = 2*F[37,x]+F[84,x]+F[90,x]
F[90,x] = F[19,x]*F[91,x]
F[91,x] = F[80,x]+F[89,x]
F[92,x] = F[19,x]*F[76,x]
F[93,x] = F[36,x]
F[94,x] = F[19,x]*F[95,x]
F[95,x] = F[1,x]+F[109,x]+F[94,x]+F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[19,x]*F[29,x]*F[98,x]
F[98,x] = F[1,x]+F[103,x]+F[66,x]+F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[19,x]
F[101,x] = F[102,x]+F[98,x]
F[102,x] = F[10,x]*F[19,x]*F[29,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[19,x]
F[105,x] = F[106,x]+F[12,x]
F[106,x] = F[107,x]*F[16,x]*F[19,x]
F[107,x] = F[108,x]+F[75,x]
F[108,x] = F[29,x]+F[88,x]
F[109,x] = F[110,x]*F[19,x]
F[110,x] = F[1,x]+F[109,x]+F[111,x]+F[165,x]+F[174,x]
F[111,x] = F[112,x]
F[112,x] = F[113,x]*F[19,x]*F[29,x]
F[113,x] = F[1,x]+F[114,x]+F[149,x]+F[151,x]+F[25,x]
F[114,x] = F[115,x]*F[19,x]
F[115,x] = F[116,x]+F[130,x]
F[116,x] = F[108,x]+F[117,x]
F[117,x] = F[118,x]+F[122,x]
F[118,x] = F[119,x]+F[17,x]
F[119,x] = F[120,x]+F[37,x]+F[87,x]
F[120,x] = F[121,x]*F[19,x]
F[121,x] = F[30,x]+F[86,x]
F[122,x] = F[123,x]+F[126,x]
F[123,x] = F[124,x]
F[124,x] = F[125,x]*F[19,x]
F[125,x] = F[123,x]+F[17,x]
F[126,x] = F[127,x]
F[127,x] = F[128,x]*F[19,x]
F[128,x] = F[123,x]+F[129,x]
F[129,x] = F[127,x]
F[130,x] = F[131,x]+F[132,x]
F[131,x] = F[35,x]+F[91,x]
F[132,x] = F[133,x]+F[137,x]
F[133,x] = F[134,x]+F[80,x]
F[134,x] = 2*F[37,x]+F[135,x]+F[90,x]
F[135,x] = F[136,x]*F[19,x]
F[136,x] = F[119,x]+F[134,x]
F[137,x] = F[138,x]+F[141,x]
F[138,x] = F[139,x]
F[139,x] = F[140,x]*F[19,x]
F[140,x] = F[123,x]+F[138,x]
F[141,x] = 3*F[37,x]+F[142,x]+F[144,x]
F[142,x] = F[143,x]*F[19,x]
F[143,x] = F[126,x]+F[141,x]
F[144,x] = F[145,x]*F[19,x]
F[145,x] = F[138,x]+F[146,x]
F[146,x] = 3*F[37,x]+F[144,x]+F[147,x]
F[147,x] = F[148,x]*F[19,x]
F[148,x] = F[129,x]+F[146,x]
F[149,x] = F[150,x]
F[150,x] = F[16,x]*F[19,x]*F[34,x]
F[151,x] = F[152,x]*F[19,x]
F[152,x] = F[153,x]+F[157,x]
F[153,x] = F[154,x]+F[29,x]
F[154,x] = F[155,x]+F[19,x]
F[155,x] = F[156,x]
F[156,x] = F[19,x]*F[30,x]
F[157,x] = F[158,x]+F[35,x]
F[158,x] = F[159,x]+F[162,x]
F[159,x] = F[160,x]
F[160,x] = F[161,x]*F[19,x]
F[161,x] = F[159,x]+F[19,x]
F[162,x] = F[163,x]
F[163,x] = F[164,x]*F[19,x]
F[164,x] = F[155,x]+F[162,x]
F[165,x] = F[166,x]*F[19,x]
F[166,x] = 2*F[165,x]+F[1,x]+F[167,x]
F[167,x] = F[168,x]
F[168,x] = F[169,x]*F[19,x]*F[29,x]
F[169,x] = F[1,x]+F[151,x]+F[170,x]+F[25,x]
F[170,x] = F[171,x]*F[19,x]
F[171,x] = F[172,x]+F[173,x]
F[172,x] = F[118,x]+F[29,x]
F[173,x] = F[133,x]+F[35,x]
F[174,x] = F[175,x]*F[19,x]
F[175,x] = F[1,x]+F[174,x]+F[176,x]+F[42,x]
F[176,x] = F[177,x]
F[177,x] = F[178,x]*F[19,x]*F[29,x]
F[178,x] = F[179,x]+F[46,x]
F[179,x] = F[16,x]^2*F[17,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_{19}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{94}\! \left(x \right)
F_{4}\! \left(x \right) = F_{19}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)+F_{60}\! \left(x \right)+F_{61}\! \left(x \right)
F_{6}\! \left(x \right) = F_{19}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{51}\! \left(x \right)+F_{52}\! \left(x \right)+F_{54}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{19}\! \left(x \right) F_{29}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)+F_{8}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)+F_{13}\! \left(x \right)+F_{42}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{19}\! \left(x \right) F_{29}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{20}\! \left(x \right)+F_{41}\! \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_{16}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = x
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right) F_{24}\! \left(x \right) F_{29}\! \left(x \right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)+F_{33}\! \left(x \right)
F_{25}\! \left(x \right) = F_{19}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{19}\! \left(x \right) F_{24}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{19}\! \left(x \right) F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{19}\! \left(x \right) F_{26}\! \left(x \right)
F_{33}\! \left(x \right) = F_{19}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{29}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{17}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = 0
F_{38}\! \left(x \right) = F_{19}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{30}\! \left(x \right)+F_{36}\! \left(x \right)
F_{40}\! \left(x \right) = F_{19}\! \left(x \right) F_{35}\! \left(x \right)
F_{41}\! \left(x \right) = F_{15}\! \left(x \right) F_{19}\! \left(x \right)
F_{42}\! \left(x \right) = F_{19}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{1}\! \left(x \right)+F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{19}\! \left(x \right) F_{29}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{47}\! \left(x \right) = F_{1}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{19}\! \left(x \right) F_{29}\! \left(x \right) F_{47}\! \left(x \right)
F_{50}\! \left(x \right) = F_{16}\! \left(x \right) F_{17}\! \left(x \right)
F_{51}\! \left(x \right) = F_{19}\! \left(x \right) F_{7}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{19}\! \left(x \right) F_{34}\! \left(x \right) F_{47}\! \left(x \right)
F_{54}\! \left(x \right) = F_{19}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)+F_{32}\! \left(x \right)+F_{54}\! \left(x \right)+F_{56}\! \left(x \right)+F_{58}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{47}\! \left(x \right)
F_{58}\! \left(x \right) = F_{19}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = 2 F_{56}\! \left(x \right)+F_{1}\! \left(x \right)+F_{44}\! \left(x \right)+F_{58}\! \left(x \right)
F_{60}\! \left(x \right) = F_{19}\! \left(x \right) F_{5}\! \left(x \right)
F_{61}\! \left(x \right) = F_{19}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{69}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{68}\! \left(x \right)
F_{64}\! \left(x \right) = F_{1}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{29}\! \left(x \right)
F_{68}\! \left(x \right) = F_{30}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{93}\! \left(x \right)
F_{70}\! \left(x \right) = F_{17}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{37}\! \left(x \right)+F_{72}\! \left(x \right)+F_{74}\! \left(x \right)
F_{72}\! \left(x \right) = F_{19}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{65}\! \left(x \right)+F_{71}\! \left(x \right)
F_{74}\! \left(x \right) = F_{19}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{35}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{83}\! \left(x \right)
F_{77}\! \left(x \right) = F_{37}\! \left(x \right)+F_{78}\! \left(x \right)+F_{81}\! \left(x \right)
F_{78}\! \left(x \right) = F_{19}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{17}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{78}\! \left(x \right)
F_{81}\! \left(x \right) = F_{19}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{17}\! \left(x \right)+F_{77}\! \left(x \right)
F_{83}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{84}\! \left(x \right)+F_{92}\! \left(x \right)
F_{84}\! \left(x \right) = F_{19}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{89}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{19}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{17}\! \left(x \right)+F_{86}\! \left(x \right)
F_{89}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{84}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{19}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{80}\! \left(x \right)+F_{89}\! \left(x \right)
F_{92}\! \left(x \right) = F_{19}\! \left(x \right) F_{76}\! \left(x \right)
F_{93}\! \left(x \right) = F_{36}\! \left(x \right)
F_{94}\! \left(x \right) = F_{19}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{1}\! \left(x \right)+F_{109}\! \left(x \right)+F_{94}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{19}\! \left(x \right) F_{29}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{1}\! \left(x \right)+F_{103}\! \left(x \right)+F_{66}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{19}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{98}\! \left(x \right)
F_{102}\! \left(x \right) = F_{10}\! \left(x \right) F_{19}\! \left(x \right) F_{29}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{19}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{12}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{75}\! \left(x \right)
F_{108}\! \left(x \right) = F_{29}\! \left(x \right)+F_{88}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{19}\! \left(x \right)
F_{110}\! \left(x \right) = F_{1}\! \left(x \right)+F_{109}\! \left(x \right)+F_{111}\! \left(x \right)+F_{165}\! \left(x \right)+F_{174}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{19}\! \left(x \right) F_{29}\! \left(x \right)
F_{113}\! \left(x \right) = F_{1}\! \left(x \right)+F_{114}\! \left(x \right)+F_{149}\! \left(x \right)+F_{151}\! \left(x \right)+F_{25}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{19}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{130}\! \left(x \right)
F_{116}\! \left(x \right) = F_{108}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{122}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{17}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{37}\! \left(x \right)+F_{87}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{19}\! \left(x \right)
F_{121}\! \left(x \right) = F_{30}\! \left(x \right)+F_{86}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{126}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{19}\! \left(x \right)
F_{125}\! \left(x \right) = F_{123}\! \left(x \right)+F_{17}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{19}\! \left(x \right)
F_{128}\! \left(x \right) = F_{123}\! \left(x \right)+F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{127}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{132}\! \left(x \right)
F_{131}\! \left(x \right) = F_{35}\! \left(x \right)+F_{91}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{137}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{80}\! \left(x \right)
F_{134}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{135}\! \left(x \right)+F_{90}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{19}\! \left(x \right)
F_{136}\! \left(x \right) = F_{119}\! \left(x \right)+F_{134}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{141}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{19}\! \left(x \right)
F_{140}\! \left(x \right) = F_{123}\! \left(x \right)+F_{138}\! \left(x \right)
F_{141}\! \left(x \right) = 3 F_{37}\! \left(x \right)+F_{142}\! \left(x \right)+F_{144}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right) F_{19}\! \left(x \right)
F_{143}\! \left(x \right) = F_{126}\! \left(x \right)+F_{141}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right) F_{19}\! \left(x \right)
F_{145}\! \left(x \right) = F_{138}\! \left(x \right)+F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = 3 F_{37}\! \left(x \right)+F_{144}\! \left(x \right)+F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{19}\! \left(x \right)
F_{148}\! \left(x \right) = F_{129}\! \left(x \right)+F_{146}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{34}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{19}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{157}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{29}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{19}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{19}\! \left(x \right) F_{30}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{35}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{162}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right) F_{19}\! \left(x \right)
F_{161}\! \left(x \right) = F_{159}\! \left(x \right)+F_{19}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right) F_{19}\! \left(x \right)
F_{164}\! \left(x \right) = F_{155}\! \left(x \right)+F_{162}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{19}\! \left(x \right)
F_{166}\! \left(x \right) = 2 F_{165}\! \left(x \right)+F_{1}\! \left(x \right)+F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right) F_{19}\! \left(x \right) F_{29}\! \left(x \right)
F_{169}\! \left(x \right) = F_{1}\! \left(x \right)+F_{151}\! \left(x \right)+F_{170}\! \left(x \right)+F_{25}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right) F_{19}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{173}\! \left(x \right)
F_{172}\! \left(x \right) = F_{118}\! \left(x \right)+F_{29}\! \left(x \right)
F_{173}\! \left(x \right) = F_{133}\! \left(x \right)+F_{35}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right) F_{19}\! \left(x \right)
F_{175}\! \left(x \right) = F_{1}\! \left(x \right)+F_{174}\! \left(x \right)+F_{176}\! \left(x \right)+F_{42}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right) F_{19}\! \left(x \right) F_{29}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)+F_{46}\! \left(x \right)
F_{179}\! \left(x \right) = F_{16} \left(x \right)^{2} F_{17}\! \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_19(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_94(x))
Eq(F_4(x), F_19(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_6(x) + F_60(x) + F_61(x))
Eq(F_6(x), F_19(x)*F_7(x))
Eq(F_7(x), F_1(x) + F_51(x) + F_52(x) + F_54(x) + F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_19(x)*F_29(x))
Eq(F_10(x), F_1(x) + F_11(x) + F_8(x))
Eq(F_11(x), F_12(x)*F_19(x))
Eq(F_12(x), F_1(x) + F_11(x) + F_13(x) + F_42(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_19(x)*F_29(x))
Eq(F_15(x), F_16(x) + F_20(x) + F_41(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_16(x)*F_19(x))
Eq(F_19(x), x)
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_19(x)*F_22(x))
Eq(F_22(x), F_15(x) + F_23(x))
Eq(F_23(x), F_19(x)*F_24(x)*F_29(x))
Eq(F_24(x), F_1(x) + F_25(x) + F_33(x))
Eq(F_25(x), F_19(x)*F_26(x))
Eq(F_26(x), F_1(x) + F_27(x) + 2*F_32(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_19(x)*F_24(x)*F_29(x))
Eq(F_29(x), F_1(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_19(x)*F_29(x))
Eq(F_32(x), F_19(x)*F_26(x))
Eq(F_33(x), F_19(x)*F_34(x))
Eq(F_34(x), F_29(x) + F_35(x))
Eq(F_35(x), F_17(x) + F_36(x))
Eq(F_36(x), F_37(x) + F_38(x) + F_40(x))
Eq(F_37(x), 0)
Eq(F_38(x), F_19(x)*F_39(x))
Eq(F_39(x), F_30(x) + F_36(x))
Eq(F_40(x), F_19(x)*F_35(x))
Eq(F_41(x), F_15(x)*F_19(x))
Eq(F_42(x), F_19(x)*F_43(x))
Eq(F_43(x), F_1(x) + F_42(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_19(x)*F_29(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_50(x))
Eq(F_47(x), F_1(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_19(x)*F_29(x)*F_47(x))
Eq(F_50(x), F_16(x)*F_17(x))
Eq(F_51(x), F_19(x)*F_7(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_19(x)*F_34(x)*F_47(x))
Eq(F_54(x), F_19(x)*F_55(x))
Eq(F_55(x), F_1(x) + F_13(x) + F_32(x) + F_54(x) + F_56(x) + F_58(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_16(x)*F_19(x)*F_47(x))
Eq(F_58(x), F_19(x)*F_59(x))
Eq(F_59(x), F_1(x) + F_44(x) + 2*F_56(x) + F_58(x))
Eq(F_60(x), F_19(x)*F_5(x))
Eq(F_61(x), F_19(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_69(x))
Eq(F_63(x), F_64(x) + F_68(x))
Eq(F_64(x), F_1(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_16(x)*F_19(x)*F_29(x))
Eq(F_68(x), F_30(x))
Eq(F_69(x), F_70(x) + F_93(x))
Eq(F_70(x), F_17(x) + F_71(x))
Eq(F_71(x), F_37(x) + F_72(x) + F_74(x))
Eq(F_72(x), F_19(x)*F_73(x))
Eq(F_73(x), F_65(x) + F_71(x))
Eq(F_74(x), F_19(x)*F_75(x))
Eq(F_75(x), F_35(x) + F_76(x))
Eq(F_76(x), F_77(x) + F_83(x))
Eq(F_77(x), F_37(x) + F_78(x) + F_81(x))
Eq(F_78(x), F_19(x)*F_79(x))
Eq(F_79(x), F_17(x) + F_80(x))
Eq(F_80(x), F_78(x))
Eq(F_81(x), F_19(x)*F_82(x))
Eq(F_82(x), F_17(x) + F_77(x))
Eq(F_83(x), 2*F_37(x) + F_84(x) + F_92(x))
Eq(F_84(x), F_19(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_89(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_19(x)*F_88(x))
Eq(F_88(x), F_17(x) + F_86(x))
Eq(F_89(x), 2*F_37(x) + F_84(x) + F_90(x))
Eq(F_90(x), F_19(x)*F_91(x))
Eq(F_91(x), F_80(x) + F_89(x))
Eq(F_92(x), F_19(x)*F_76(x))
Eq(F_93(x), F_36(x))
Eq(F_94(x), F_19(x)*F_95(x))
Eq(F_95(x), F_1(x) + F_109(x) + F_94(x) + F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_19(x)*F_29(x)*F_98(x))
Eq(F_98(x), F_1(x) + F_103(x) + F_66(x) + F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_19(x))
Eq(F_101(x), F_102(x) + F_98(x))
Eq(F_102(x), F_10(x)*F_19(x)*F_29(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_19(x))
Eq(F_105(x), F_106(x) + F_12(x))
Eq(F_106(x), F_107(x)*F_16(x)*F_19(x))
Eq(F_107(x), F_108(x) + F_75(x))
Eq(F_108(x), F_29(x) + F_88(x))
Eq(F_109(x), F_110(x)*F_19(x))
Eq(F_110(x), F_1(x) + F_109(x) + F_111(x) + F_165(x) + F_174(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x)*F_19(x)*F_29(x))
Eq(F_113(x), F_1(x) + F_114(x) + F_149(x) + F_151(x) + F_25(x))
Eq(F_114(x), F_115(x)*F_19(x))
Eq(F_115(x), F_116(x) + F_130(x))
Eq(F_116(x), F_108(x) + F_117(x))
Eq(F_117(x), F_118(x) + F_122(x))
Eq(F_118(x), F_119(x) + F_17(x))
Eq(F_119(x), F_120(x) + F_37(x) + F_87(x))
Eq(F_120(x), F_121(x)*F_19(x))
Eq(F_121(x), F_30(x) + F_86(x))
Eq(F_122(x), F_123(x) + F_126(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_125(x)*F_19(x))
Eq(F_125(x), F_123(x) + F_17(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x)*F_19(x))
Eq(F_128(x), F_123(x) + F_129(x))
Eq(F_129(x), F_127(x))
Eq(F_130(x), F_131(x) + F_132(x))
Eq(F_131(x), F_35(x) + F_91(x))
Eq(F_132(x), F_133(x) + F_137(x))
Eq(F_133(x), F_134(x) + F_80(x))
Eq(F_134(x), F_135(x) + 2*F_37(x) + F_90(x))
Eq(F_135(x), F_136(x)*F_19(x))
Eq(F_136(x), F_119(x) + F_134(x))
Eq(F_137(x), F_138(x) + F_141(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_140(x)*F_19(x))
Eq(F_140(x), F_123(x) + F_138(x))
Eq(F_141(x), F_142(x) + F_144(x) + 3*F_37(x))
Eq(F_142(x), F_143(x)*F_19(x))
Eq(F_143(x), F_126(x) + F_141(x))
Eq(F_144(x), F_145(x)*F_19(x))
Eq(F_145(x), F_138(x) + F_146(x))
Eq(F_146(x), F_144(x) + F_147(x) + 3*F_37(x))
Eq(F_147(x), F_148(x)*F_19(x))
Eq(F_148(x), F_129(x) + F_146(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_16(x)*F_19(x)*F_34(x))
Eq(F_151(x), F_152(x)*F_19(x))
Eq(F_152(x), F_153(x) + F_157(x))
Eq(F_153(x), F_154(x) + F_29(x))
Eq(F_154(x), F_155(x) + F_19(x))
Eq(F_155(x), F_156(x))
Eq(F_156(x), F_19(x)*F_30(x))
Eq(F_157(x), F_158(x) + F_35(x))
Eq(F_158(x), F_159(x) + F_162(x))
Eq(F_159(x), F_160(x))
Eq(F_160(x), F_161(x)*F_19(x))
Eq(F_161(x), F_159(x) + F_19(x))
Eq(F_162(x), F_163(x))
Eq(F_163(x), F_164(x)*F_19(x))
Eq(F_164(x), F_155(x) + F_162(x))
Eq(F_165(x), F_166(x)*F_19(x))
Eq(F_166(x), F_1(x) + 2*F_165(x) + F_167(x))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_169(x)*F_19(x)*F_29(x))
Eq(F_169(x), F_1(x) + F_151(x) + F_170(x) + F_25(x))
Eq(F_170(x), F_171(x)*F_19(x))
Eq(F_171(x), F_172(x) + F_173(x))
Eq(F_172(x), F_118(x) + F_29(x))
Eq(F_173(x), F_133(x) + F_35(x))
Eq(F_174(x), F_175(x)*F_19(x))
Eq(F_175(x), F_1(x) + F_174(x) + F_176(x) + F_42(x))
Eq(F_176(x), F_177(x))
Eq(F_177(x), F_178(x)*F_19(x)*F_29(x))
Eq(F_178(x), F_179(x) + F_46(x))
Eq(F_179(x), F_16(x)**2*F_17(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "row_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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{"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "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": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 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"pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1], [3, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [3, 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[1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "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": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 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, 0], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 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, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [1, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": 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