0132_0231_1203_1230
Counting sequence:
1, 1, 2, 6, 20, 69, 241, 847, 2992, 10625, 37942, 136268, 492176, 1787330, 6523973, 23927061, 88141152, 326007129, 1210293258, 4508549976, 16847893392, 63140527014, 237261390378, 893746947390, 3374364517920, 12766991584634, 48399463524396, 183818985793992, 699336081748128, 2664894368219172, 10170201750940717, 38868291048782145, 148744803455024320, 569948751537919561, 2186489067481386114, 8397471989988540352, 32285980094682334352, 124256721279319748734, 478679036190978224894, 1845725920717912817874, 7123106186917192342688, 27512715223648142659806, 106351330057667609261812, 411417283325246846414024, 1592714590447017946179808, 6170151090176373097160156, 23919025391505772364030242, 92783167322596868253602834, 360132103901151698510651200, 1398656152746760320550805450, 5435089594856419976092328932, 21131960194275220915827567248, 82205600690287470348619585696, 319950853262212044908241162044, 1245883745015174789017098946036, 4853742132648890971251081901436, 18917935853727697624635759565120, 73766972665334071694141012256980, 287763008376583047329371294805848, 1123017963688024936316336455260752, 4384412522138577062487223988543296, 17123935845632877098867566096421576, 66904913973474444766823530415797117, 261498793673956007649785784951331097, 1022430614245880038485193647352373632, 3998949582792175144516916018303010089, 15645937410285952225676608278889718578, 61234568349632343588578540896764120656, 239732635671952527747107142779748295312, 938834995209503453302817811097895528174, 3677725670825737319942131230866584279798, 14410990671752906389979541008928012900746, 56484517280326919880728262156241273496992, 221453655631297721541807159876758090702774, 868462419100109647319253643901494806858148, 3406677072529516034914475675579236681537736, 13366564511328659213575139157558540300806752, 52458366660056352172034358027283541052457004, 205926960184036693658376442869896087576774998, 808560599285869993229703167086194443313408406, 3175487433457048993576626540868853905413078592, 12473958807285321018907651615114808042794262894, 49010824222529810934492783429158895229716724588, 192606656067359388960970913781805593540441925136, 757076959188750872390092059291003585191547591392, 2976433344113215012725166847166153738340893638324, 11704091257027435172892822023380255595788659257228, 46032305040012279958131201648916372682290481814756, 181079536222510942188349525711590712891390159348672, 712452404670234678678162109634727825667594772695404, 2803628296545648375663390284494716680732251164354408, 11034722758127880869536391874771970145794713224348016, 43438738450488163858056674334028716642702964242724032, 171027596224431859759480234903838546570031399827011064, 673483349120249853960615810590067475510376602111277778, 2652514323214983064513653540860686617339159552965558906, 10448582639778457819888869268527068487930934653676368512, 41164647891604027674189940817429448747325518715932567274, 162202467876486528152106205358354001312346928363557164788, 639227177243489644133282382973170753083734838759850563776, 2519512137620078038454764447375888717671026449016846290592
Generating function in Maple syntax:
((-x^3+2*x^2-3*x+1)*(1-4*x)^(1/2)+5*x^3-8*x^2+5*x-1)/(4*x^3-2*x^2)
Generating function in latex syntax:
\frac{\left(-x^{3}+2 x^{2}-3 x +1\right) \sqrt{1-4 x}+5 x^{3}-8 x^{2}+5 x -1}{4 x^{3}-2 x^{2}}
Generating function in sympy syntax:
(5*x**3 - 8*x**2 + 5*x + sqrt(1 - 4*x)*(-x**3 + 2*x**2 - 3*x + 1) - 1)/(4*x**3 - 2*x**2)
Implicit equation for the generating function in Maple syntax:
x^2*(2*x-1)^2*F(x)^2-(2*x-1)*(5*x^3-8*x^2+5*x-1)*F(x)+x^5+2*x^4-9*x^3+12*x^2-6*x+1 = 0
Implicit equation for the generating function in latex syntax:
x^{2} \left(2 x -1\right)^{2} F \! \left(x \right)^{2}-\left(2 x -1\right) \left(5 x^{3}-8 x^{2}+5 x -1\right) F \! \left(x \right)+x^{5}+2 x^{4}-9 x^{3}+12 x^{2}-6 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 69
a(n+5) = 4*(-1+2*n)/(7+n)*a(n)+(109+37*n)/(7+n)*a(2+n)-2*(12+11*n)/(7+n)*a(n+1)-2*(61+14*n)/(7+n)*a(n+3)+3*(17+3*n)/(7+n)*a(n+4), n >= 6
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) = 69
a \! \left(n +5\right) = \frac{4 \left(-1+2 n \right) a \! \left(n \right)}{7+n}+\frac{\left(109+37 n \right) a \! \left(2+n \right)}{7+n}-\frac{2 \left(12+11 n \right) a \! \left(n +1\right)}{7+n}-\frac{2 \left(61+14 n \right) a \! \left(n +3\right)}{7+n}+\frac{3 \left(17+3 n \right) a \! \left(n +4\right)}{7+n}, \quad n \geq 6
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21228/
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[153,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[14,x]+F[72,x,k[0]]
F[14,x] = F[15,x]+F[33,x]
F[15,x] = F[16,x]+F[32,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[27,x]
F[24,x] = F[25,x]
F[25,x] = F[11,x]*F[26,x]
F[26,x] = F[1,x]+F[24,x]
F[27,x] = F[28,x]+F[29,x]+F[31,x]
F[28,x] = 0
F[29,x] = F[11,x]*F[30,x]
F[30,x] = F[21,x]+F[27,x]
F[31,x] = F[11,x]*F[23,x]
F[32,x] = F[17,x]
F[33,x] = F[34,x]+F[58,x]
F[34,x] = F[24,x]+F[35,x]
F[35,x] = F[28,x]+F[36,x]+F[38,x]
F[36,x] = F[11,x]*F[37,x]
F[37,x] = F[17,x]+F[35,x]
F[38,x] = F[11,x]*F[39,x]
F[39,x] = F[23,x]+F[40,x]
F[40,x] = F[41,x]+F[46,x]
F[41,x] = F[28,x]+F[42,x]+F[44,x]
F[42,x] = F[11,x]*F[43,x]
F[43,x] = F[24,x]+F[41,x]
F[44,x] = F[11,x]*F[45,x]
F[45,x] = F[24,x]+F[41,x]
F[46,x] = F[28,x]+F[47,x]+F[55,x]+F[57,x]
F[47,x] = F[11,x]*F[48,x]
F[48,x] = F[49,x]+F[52,x]
F[49,x] = F[50,x]
F[50,x] = F[11,x]*F[51,x]
F[51,x] = F[24,x]+F[49,x]
F[52,x] = 2*F[28,x]+F[47,x]+F[53,x]
F[53,x] = F[11,x]*F[54,x]
F[54,x] = F[41,x]+F[52,x]
F[55,x] = F[11,x]*F[56,x]
F[56,x] = F[27,x]+F[46,x]
F[57,x] = F[11,x]*F[40,x]
F[58,x] = F[59,x]
F[59,x] = F[28,x]+F[60,x]+F[62,x]
F[60,x] = F[11,x]*F[61,x]
F[61,x] = F[17,x]+F[59,x]
F[62,x] = F[11,x]*F[63,x]
F[63,x] = F[23,x]+F[64,x]
F[64,x] = F[65,x]+F[68,x]
F[65,x] = F[66,x]
F[66,x] = F[11,x]*F[67,x]
F[67,x] = F[24,x]+F[65,x]
F[68,x] = 2*F[28,x]+F[69,x]+F[71,x]
F[69,x] = F[11,x]*F[70,x]
F[70,x] = F[27,x]+F[68,x]
F[71,x] = F[11,x]*F[64,x]
F[72,x,k[0]] = F[117,x,k[0]]+F[73,x,k[0]]
F[73,x,k[0]] = F[103,x,k[0]]+F[74,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]+F[78,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]*F[8,x,k[0]]
F[77,x,k[0]] = F[1,x]+F[75,x,k[0]]
F[78,x,k[0]] = F[28,x]+F[79,x,k[0]]+F[81,x,k[0]]
F[79,x,k[0]] = F[8,x,k[0]]*F[80,x,k[0]]
F[80,x,k[0]] = F[17,x]+F[78,x,k[0]]
F[81,x,k[0]] = F[11,x]*F[82,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]+F[88,x,k[0]]
F[83,x,k[0]] = F[75,x,k[0]]+F[84,x,k[0]]
F[84,x,k[0]] = F[28,x]+F[85,x,k[0]]+F[87,x,k[0]]
F[85,x,k[0]] = F[8,x,k[0]]*F[86,x,k[0]]
F[86,x,k[0]] = F[21,x]+F[84,x,k[0]]
F[87,x,k[0]] = F[11,x]*F[83,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]+F[94,x,k[0]]
F[89,x,k[0]] = F[28,x]+F[90,x,k[0]]+F[92,x,k[0]]
F[90,x,k[0]] = F[8,x,k[0]]*F[91,x,k[0]]
F[91,x,k[0]] = F[24,x]+F[89,x,k[0]]
F[92,x,k[0]] = F[11,x]*F[93,x,k[0]]
F[93,x,k[0]] = F[75,x,k[0]]+F[89,x,k[0]]
F[94,x,k[0]] = F[100,x,k[0]]+F[102,x,k[0]]+F[28,x]+F[95,x,k[0]]
F[95,x,k[0]] = F[8,x,k[0]]*F[96,x,k[0]]
F[96,x,k[0]] = F[49,x]+F[97,x,k[0]]
F[97,x,k[0]] = 2*F[28,x]+F[95,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[11,x]*F[99,x,k[0]]
F[99,x,k[0]] = F[89,x,k[0]]+F[97,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]*F[11,x]
F[101,x,k[0]] = F[84,x,k[0]]+F[94,x,k[0]]
F[102,x,k[0]] = F[11,x]*F[88,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]+F[107,x,k[0]]+F[28,x]
F[105,x,k[0]] = F[106,x,k[0]]*F[8,x,k[0]]
F[106,x,k[0]] = F[104,x,k[0]]+F[17,x]
F[107,x,k[0]] = F[108,x,k[0]]*F[11,x]
F[108,x,k[0]] = F[109,x,k[0]]+F[83,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]+F[113,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]
F[111,x,k[0]] = F[11,x]*F[112,x,k[0]]
F[112,x,k[0]] = F[110,x,k[0]]+F[75,x,k[0]]
F[113,x,k[0]] = 2*F[28,x]+F[114,x,k[0]]+F[116,x,k[0]]
F[114,x,k[0]] = F[11,x]*F[115,x,k[0]]
F[115,x,k[0]] = F[113,x,k[0]]+F[84,x,k[0]]
F[116,x,k[0]] = F[109,x,k[0]]*F[11,x]
F[117,x,k[0]] = F[118,x,k[0]]+F[139,x,k[0]]
F[118,x,k[0]] = F[110,x,k[0]]+F[119,x,k[0]]
F[119,x,k[0]] = 2*F[28,x]+F[120,x,k[0]]+F[122,x,k[0]]
F[120,x,k[0]] = F[11,x]*F[121,x,k[0]]
F[121,x,k[0]] = F[119,x,k[0]]+F[78,x,k[0]]
F[122,x,k[0]] = F[11,x]*F[123,x,k[0]]
F[123,x,k[0]] = F[109,x,k[0]]+F[124,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]+F[130,x,k[0]]
F[125,x,k[0]] = 2*F[28,x]+F[126,x,k[0]]+F[128,x,k[0]]
F[126,x,k[0]] = F[11,x]*F[127,x,k[0]]
F[127,x,k[0]] = F[125,x,k[0]]+F[89,x,k[0]]
F[128,x,k[0]] = F[11,x]*F[129,x,k[0]]
F[129,x,k[0]] = F[110,x,k[0]]+F[125,x,k[0]]
F[130,x,k[0]] = 2*F[28,x]+F[131,x,k[0]]+F[136,x,k[0]]+F[138,x,k[0]]
F[131,x,k[0]] = F[11,x]*F[132,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]+F[97,x,k[0]]
F[133,x,k[0]] = 3*F[28,x]+F[131,x,k[0]]+F[134,x,k[0]]
F[134,x,k[0]] = F[11,x]*F[135,x,k[0]]
F[135,x,k[0]] = F[125,x,k[0]]+F[133,x,k[0]]
F[136,x,k[0]] = F[11,x]*F[137,x,k[0]]
F[137,x,k[0]] = F[113,x,k[0]]+F[130,x,k[0]]
F[138,x,k[0]] = F[11,x]*F[124,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]
F[140,x,k[0]] = 2*F[28,x]+F[141,x,k[0]]+F[143,x,k[0]]
F[141,x,k[0]] = F[11,x]*F[142,x,k[0]]
F[142,x,k[0]] = F[104,x,k[0]]+F[140,x,k[0]]
F[143,x,k[0]] = F[11,x]*F[144,x,k[0]]
F[144,x,k[0]] = F[109,x,k[0]]+F[145,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]+F[149,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]
F[147,x,k[0]] = F[11,x]*F[148,x,k[0]]
F[148,x,k[0]] = F[110,x,k[0]]+F[146,x,k[0]]
F[149,x,k[0]] = 3*F[28,x]+F[150,x,k[0]]+F[152,x,k[0]]
F[150,x,k[0]] = F[11,x]*F[151,x,k[0]]
F[151,x,k[0]] = F[113,x,k[0]]+F[149,x,k[0]]
F[152,x,k[0]] = F[11,x]*F[145,x,k[0]]
F[153,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_{153}\! \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{F_{6}\! \left(x , y\right) y -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_{14}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{33}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{32}\! \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_{27}\! \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_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = 0
F_{29}\! \left(x \right) = F_{11}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{21}\! \left(x \right)+F_{27}\! \left(x \right)
F_{31}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{32}\! \left(x \right) = F_{17}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{58}\! \left(x \right)
F_{34}\! \left(x \right) = F_{24}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{28}\! \left(x \right)+F_{36}\! \left(x \right)+F_{38}\! \left(x \right)
F_{36}\! \left(x \right) = F_{11}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{17}\! \left(x \right)+F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{11}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{23}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{46}\! \left(x \right)
F_{41}\! \left(x \right) = F_{28}\! \left(x \right)+F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{11}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{24}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{24}\! \left(x \right)+F_{41}\! \left(x \right)
F_{46}\! \left(x \right) = F_{28}\! \left(x \right)+F_{47}\! \left(x \right)+F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{47}\! \left(x \right) = F_{11}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{52}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{24}\! \left(x \right)+F_{49}\! \left(x \right)
F_{52}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{47}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{41}\! \left(x \right)+F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{11}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{27}\! \left(x \right)+F_{46}\! \left(x \right)
F_{57}\! \left(x \right) = F_{11}\! \left(x \right) F_{40}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{28}\! \left(x \right)+F_{60}\! \left(x \right)+F_{62}\! \left(x \right)
F_{60}\! \left(x \right) = F_{11}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{17}\! \left(x \right)+F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = F_{11}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{23}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{68}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{11}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{24}\! \left(x \right)+F_{65}\! \left(x \right)
F_{68}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{69}\! \left(x \right)+F_{71}\! \left(x \right)
F_{69}\! \left(x \right) = F_{11}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{27}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{11}\! \left(x \right) F_{64}\! \left(x \right)
F_{72}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{75}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{79}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{78}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{85}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{21}\! \left(x \right)+F_{84}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{90}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{89}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{102}\! \left(x , y\right)+F_{28}\! \left(x \right)+F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{49}\! \left(x \right)+F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = 2 F_{28}\! \left(x \right)+F_{95}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{89}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{101}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{88}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{107}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{17}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{113}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{112}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = 2 F_{28}\! \left(x \right)+F_{114}\! \left(x , y\right)+F_{116}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{115}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{139}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{119}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = 2 F_{28}\! \left(x \right)+F_{120}\! \left(x , y\right)+F_{122}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{121}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{130}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = 2 F_{28}\! \left(x \right)+F_{126}\! \left(x , y\right)+F_{128}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{127}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{129}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{125}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = 2 F_{28}\! \left(x \right)+F_{131}\! \left(x , y\right)+F_{136}\! \left(x , y\right)+F_{138}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{132}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = 3 F_{28}\! \left(x \right)+F_{131}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{135}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{137}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{130}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{124}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = 2 F_{28}\! \left(x \right)+F_{141}\! \left(x , y\right)+F_{143}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{140}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{144}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)+F_{149}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{148}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{146}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = 3 F_{28}\! \left(x \right)+F_{150}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{151}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{149}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{145}\! \left(x , y\right)
F_{153}\! \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_153(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_14(x) + F_72(x, k_0))
Eq(F_14(x), F_15(x) + F_33(x))
Eq(F_15(x), F_16(x) + F_32(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_27(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_11(x)*F_26(x))
Eq(F_26(x), F_1(x) + F_24(x))
Eq(F_27(x), F_28(x) + F_29(x) + F_31(x))
Eq(F_28(x), 0)
Eq(F_29(x), F_11(x)*F_30(x))
Eq(F_30(x), F_21(x) + F_27(x))
Eq(F_31(x), F_11(x)*F_23(x))
Eq(F_32(x), F_17(x))
Eq(F_33(x), F_34(x) + F_58(x))
Eq(F_34(x), F_24(x) + F_35(x))
Eq(F_35(x), F_28(x) + F_36(x) + F_38(x))
Eq(F_36(x), F_11(x)*F_37(x))
Eq(F_37(x), F_17(x) + F_35(x))
Eq(F_38(x), F_11(x)*F_39(x))
Eq(F_39(x), F_23(x) + F_40(x))
Eq(F_40(x), F_41(x) + F_46(x))
Eq(F_41(x), F_28(x) + F_42(x) + F_44(x))
Eq(F_42(x), F_11(x)*F_43(x))
Eq(F_43(x), F_24(x) + F_41(x))
Eq(F_44(x), F_11(x)*F_45(x))
Eq(F_45(x), F_24(x) + F_41(x))
Eq(F_46(x), F_28(x) + F_47(x) + F_55(x) + F_57(x))
Eq(F_47(x), F_11(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_52(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_11(x)*F_51(x))
Eq(F_51(x), F_24(x) + F_49(x))
Eq(F_52(x), 2*F_28(x) + F_47(x) + F_53(x))
Eq(F_53(x), F_11(x)*F_54(x))
Eq(F_54(x), F_41(x) + F_52(x))
Eq(F_55(x), F_11(x)*F_56(x))
Eq(F_56(x), F_27(x) + F_46(x))
Eq(F_57(x), F_11(x)*F_40(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_28(x) + F_60(x) + F_62(x))
Eq(F_60(x), F_11(x)*F_61(x))
Eq(F_61(x), F_17(x) + F_59(x))
Eq(F_62(x), F_11(x)*F_63(x))
Eq(F_63(x), F_23(x) + F_64(x))
Eq(F_64(x), F_65(x) + F_68(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_11(x)*F_67(x))
Eq(F_67(x), F_24(x) + F_65(x))
Eq(F_68(x), 2*F_28(x) + F_69(x) + F_71(x))
Eq(F_69(x), F_11(x)*F_70(x))
Eq(F_70(x), F_27(x) + F_68(x))
Eq(F_71(x), F_11(x)*F_64(x))
Eq(F_72(x, k_0), F_117(x, k_0) + F_73(x, k_0))
Eq(F_73(x, k_0), F_103(x, k_0) + F_74(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0) + F_78(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0)*F_8(x, k_0))
Eq(F_77(x, k_0), F_1(x) + F_75(x, k_0))
Eq(F_78(x, k_0), F_28(x) + F_79(x, k_0) + F_81(x, k_0))
Eq(F_79(x, k_0), F_8(x, k_0)*F_80(x, k_0))
Eq(F_80(x, k_0), F_17(x) + F_78(x, k_0))
Eq(F_81(x, k_0), F_11(x)*F_82(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0) + F_88(x, k_0))
Eq(F_83(x, k_0), F_75(x, k_0) + F_84(x, k_0))
Eq(F_84(x, k_0), F_28(x) + F_85(x, k_0) + F_87(x, k_0))
Eq(F_85(x, k_0), F_8(x, k_0)*F_86(x, k_0))
Eq(F_86(x, k_0), F_21(x) + F_84(x, k_0))
Eq(F_87(x, k_0), F_11(x)*F_83(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0) + F_94(x, k_0))
Eq(F_89(x, k_0), F_28(x) + F_90(x, k_0) + F_92(x, k_0))
Eq(F_90(x, k_0), F_8(x, k_0)*F_91(x, k_0))
Eq(F_91(x, k_0), F_24(x) + F_89(x, k_0))
Eq(F_92(x, k_0), F_11(x)*F_93(x, k_0))
Eq(F_93(x, k_0), F_75(x, k_0) + F_89(x, k_0))
Eq(F_94(x, k_0), F_100(x, k_0) + F_102(x, k_0) + F_28(x) + F_95(x, k_0))
Eq(F_95(x, k_0), F_8(x, k_0)*F_96(x, k_0))
Eq(F_96(x, k_0), F_49(x) + F_97(x, k_0))
Eq(F_97(x, k_0), 2*F_28(x) + F_95(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_11(x)*F_99(x, k_0))
Eq(F_99(x, k_0), F_89(x, k_0) + F_97(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0)*F_11(x))
Eq(F_101(x, k_0), F_84(x, k_0) + F_94(x, k_0))
Eq(F_102(x, k_0), F_11(x)*F_88(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0) + F_107(x, k_0) + F_28(x))
Eq(F_105(x, k_0), F_106(x, k_0)*F_8(x, k_0))
Eq(F_106(x, k_0), F_104(x, k_0) + F_17(x))
Eq(F_107(x, k_0), F_108(x, k_0)*F_11(x))
Eq(F_108(x, k_0), F_109(x, k_0) + F_83(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0) + F_113(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0))
Eq(F_111(x, k_0), F_11(x)*F_112(x, k_0))
Eq(F_112(x, k_0), F_110(x, k_0) + F_75(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0) + F_116(x, k_0) + 2*F_28(x))
Eq(F_114(x, k_0), F_11(x)*F_115(x, k_0))
Eq(F_115(x, k_0), F_113(x, k_0) + F_84(x, k_0))
Eq(F_116(x, k_0), F_109(x, k_0)*F_11(x))
Eq(F_117(x, k_0), F_118(x, k_0) + F_139(x, k_0))
Eq(F_118(x, k_0), F_110(x, k_0) + F_119(x, k_0))
Eq(F_119(x, k_0), F_120(x, k_0) + F_122(x, k_0) + 2*F_28(x))
Eq(F_120(x, k_0), F_11(x)*F_121(x, k_0))
Eq(F_121(x, k_0), F_119(x, k_0) + F_78(x, k_0))
Eq(F_122(x, k_0), F_11(x)*F_123(x, k_0))
Eq(F_123(x, k_0), F_109(x, k_0) + F_124(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0) + F_130(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0) + F_128(x, k_0) + 2*F_28(x))
Eq(F_126(x, k_0), F_11(x)*F_127(x, k_0))
Eq(F_127(x, k_0), F_125(x, k_0) + F_89(x, k_0))
Eq(F_128(x, k_0), F_11(x)*F_129(x, k_0))
Eq(F_129(x, k_0), F_110(x, k_0) + F_125(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0) + F_136(x, k_0) + F_138(x, k_0) + 2*F_28(x))
Eq(F_131(x, k_0), F_11(x)*F_132(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0) + F_97(x, k_0))
Eq(F_133(x, k_0), F_131(x, k_0) + F_134(x, k_0) + 3*F_28(x))
Eq(F_134(x, k_0), F_11(x)*F_135(x, k_0))
Eq(F_135(x, k_0), F_125(x, k_0) + F_133(x, k_0))
Eq(F_136(x, k_0), F_11(x)*F_137(x, k_0))
Eq(F_137(x, k_0), F_113(x, k_0) + F_130(x, k_0))
Eq(F_138(x, k_0), F_11(x)*F_124(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0) + F_143(x, k_0) + 2*F_28(x))
Eq(F_141(x, k_0), F_11(x)*F_142(x, k_0))
Eq(F_142(x, k_0), F_104(x, k_0) + F_140(x, k_0))
Eq(F_143(x, k_0), F_11(x)*F_144(x, k_0))
Eq(F_144(x, k_0), F_109(x, k_0) + F_145(x, k_0))
Eq(F_145(x, k_0), F_146(x, k_0) + F_149(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0))
Eq(F_147(x, k_0), F_11(x)*F_148(x, k_0))
Eq(F_148(x, k_0), F_110(x, k_0) + F_146(x, k_0))
Eq(F_149(x, k_0), F_150(x, k_0) + F_152(x, k_0) + 3*F_28(x))
Eq(F_150(x, k_0), F_11(x)*F_151(x, k_0))
Eq(F_151(x, k_0), F_113(x, k_0) + F_149(x, k_0))
Eq(F_152(x, k_0), F_11(x)*F_145(x, k_0))
Eq(F_153(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, 3, 1], "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, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 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, 3, 1], "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, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 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, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 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}}, {"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": "BasicVerificationStrategy"}}, {"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, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", 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[0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 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], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 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, 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], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [1, 0], [3, 0]], [[2, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 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": 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0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": []}], "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": [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, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": 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