0213_0231_0312_1230
Counting sequence:
1, 1, 2, 6, 20, 68, 232, 793, 2719, 9366, 32451, 113181, 397532, 1406291, 5009981, 17969617, 64866850, 235560383, 860163419, 3156915664, 11640177613, 43101643355, 160214782052, 597637189171, 2236481705485, 8393946034088, 31588816666027, 119171348735693, 450606079459404, 1707393202793167, 6482075597709665, 24653496625378129, 93923207077019102, 358384125263825891, 1369500950039703115, 5240516135463123188, 20079274852395517417, 77028515974624264443, 295838527209240492584, 1137444711809059610899, 4377771907034478848153, 16865535516379290849940, 65035427370732041392867, 251005365977093297070881, 969573831743373839586416, 3748233744144282908766007, 14501220404068152130250485, 56143543802184873588322298, 217519761730273740339849329, 843312190083914754529850461, 3271573975918396900764259366, 12699672092673271025746194881, 49327037906845409356155110477, 191700979192100139392988147406, 745419874785843611769311149405, 2900053825718342624012206157933, 11288369296996420015832006036762, 43961093066356022332629715936393, 171281464477644247207065018759169, 667651374915909096952212146084066, 2603633634611049114875057311797701, 10157675558309853812786495078447581, 39644874866194427848221724775385682, 154793324112954155868391147101542966, 604622566230940739660089989350029916, 2362534607979154413026350629765318232, 9234825695964995896667897817307339180, 36110304332751725270348064024515359058, 141247561257337430713844829691825946594, 552680033951555970975598937178618888424, 2163243643997180801589326572124143013878, 8469776605845527452231436618808416780360, 33171836713956590299196101464565616920202, 129955442121682821560707108270728420813346, 509264389232040439838045039601730241778076, 1996239623382610667507116149504806167257422, 7827072102418337850354168173291628459436670, 30697301549955679636109977232667895482253588, 120423790705361390367243192821184296840159614, 472533664518328474000523143551081103823946284, 1854636618446430504657391422777744936770508718, 7280947084914610978571626668278951976652006730, 28590209551937538300866146504962500262582436272, 112290952672444644962444583845445884681288039626, 441131217239231125199333964251206425915982550846, 1733341499888732330551309040373312718948420456552, 6812265950138942929023215668952686271911823324090, 26778611038080473784558091270905817323297137282018, 105286198080534539201009405708385174873925942993084, 414037620335998111601430291660798991459664993201834, 1628512947119812984484773838252870369694435382510018, 6406544253006735963411946294788077898672750654450420, 25207853167224274942043684864363007538789684348629242, 99203176139022725799925017951573907145638169043204106, 390473267697240076123722018452176139120466192454336676, 1537203733893971700086015354612940661040429511578250772, 6052633542435772993992982845856013310035867523189301840, 23835739840731013947782069946853638711361114614132021248, 93882085337099475757507171909433693634642298042163862704, 369832630825594047422183584961050583480565998864387392204, 1457118092641355463872574572256440981315809854886662128548
Generating function in Maple syntax:
1/2*((2*x-1)*(-4*x+1)^(1/2)-2*x^2-2*x+1)/(x^2-3*x+1)/x
Generating function in latex syntax:
\frac{\left(2 x -1\right) \sqrt{-4 x +1}-2 x^{2}-2 x +1}{2 \left(x^{2}-3 x +1\right) x}
Generating function in sympy syntax:
(-x**2 - x + sqrt(1 - 4*x)*(2*x - 1)/2 + 1/2)/(x*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
x*(x^2-3*x+1)^2*F(x)^2+(x^2-3*x+1)*(2*x^2+2*x-1)*F(x)+x^3+6*x^2-5*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(x^{2}-3 x +1\right)^{2} F \! \left(x \right)^{2}+\left(x^{2}-3 x +1\right) \left(2 x^{2}+2 x -1\right) F \! \left(x \right)+x^{3}+6 x^{2}-5 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+4) = -4*(3+2*n)/(5+n)*a(n)+2*(28+15*n)/(5+n)*a(1+n)-(77+27*n)/(5+n)*a(n+2)+(35+9*n)/(5+n)*a(n+3), n >= 4
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(n +4\right) = -\frac{4 \left(3+2 n \right) a \! \left(n \right)}{5+n}+\frac{2 \left(28+15 n \right) a \! \left(1+n \right)}{5+n}-\frac{\left(77+27 n \right) a \! \left(n +2\right)}{5+n}+\frac{\left(35+9 n \right) a \! \left(n +3\right)}{5+n}, \quad n \geq 4
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21304/
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[173,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[89,x,k[0]]
F[14,x] = F[15,x]+F[26,x]
F[15,x] = F[16,x]+F[19,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[11,x]*F[16,x]
F[19,x] = F[20,x]+F[23,x]
F[20,x] = F[21,x]
F[21,x] = F[11,x]*F[22,x]
F[22,x] = F[1,x]+F[20,x]
F[23,x] = F[24,x]
F[24,x] = F[11,x]*F[25,x]
F[25,x] = F[17,x]+F[23,x]
F[26,x] = F[27,x]+F[58,x]
F[27,x] = F[28,x]+F[40,x]
F[28,x] = F[29,x]
F[29,x] = F[11,x]*F[30,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[1,x]+F[11,x]
F[32,x] = F[28,x]+F[33,x]
F[33,x] = F[34,x]+F[35,x]+F[39,x]
F[34,x] = 0
F[35,x] = F[11,x]*F[36,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[11,x]
F[38,x] = F[33,x]
F[39,x] = F[11,x]*F[28,x]
F[40,x] = F[34,x]+F[41,x]+F[53,x]
F[41,x] = F[11,x]*F[42,x]
F[42,x] = F[43,x]+F[46,x]
F[43,x] = F[17,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[11,x]*F[17,x]
F[46,x] = F[40,x]+F[47,x]
F[47,x] = 2*F[34,x]+F[48,x]+F[52,x]
F[48,x] = F[11,x]*F[49,x]
F[49,x] = F[50,x]+F[51,x]
F[50,x] = F[44,x]
F[51,x] = F[47,x]
F[52,x] = F[11,x]*F[40,x]
F[53,x] = F[11,x]*F[54,x]
F[54,x] = F[17,x]+F[55,x]
F[55,x] = F[34,x]+F[53,x]+F[56,x]
F[56,x] = F[11,x]*F[57,x]
F[57,x] = F[17,x]+F[55,x]
F[58,x] = F[59,x]+F[74,x]
F[59,x] = F[34,x]+F[60,x]+F[72,x]
F[60,x] = F[11,x]*F[61,x]
F[61,x] = F[62,x]+F[65,x]
F[62,x] = F[20,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[11,x]*F[20,x]
F[65,x] = F[59,x]+F[66,x]
F[66,x] = 2*F[34,x]+F[67,x]+F[71,x]
F[67,x] = F[11,x]*F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[63,x]
F[70,x] = F[66,x]
F[71,x] = F[11,x]*F[59,x]
F[72,x] = F[11,x]*F[73,x]
F[73,x] = F[28,x]+F[59,x]
F[74,x] = 2*F[34,x]+F[75,x]+F[87,x]
F[75,x] = F[11,x]*F[76,x]
F[76,x] = F[77,x]+F[80,x]
F[77,x] = F[23,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[11,x]*F[23,x]
F[80,x] = F[74,x]+F[81,x]
F[81,x] = 3*F[34,x]+F[82,x]+F[86,x]
F[82,x] = F[11,x]*F[83,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[78,x]
F[85,x] = F[81,x]
F[86,x] = F[11,x]*F[74,x]
F[87,x] = F[11,x]*F[88,x]
F[88,x] = F[40,x]+F[74,x]
F[89,x,k[0]] = F[106,x,k[0]]+F[90,x,k[0]]
F[90,x,k[0]] = F[91,x,k[0]]+F[99,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]+F[95,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]
F[93,x,k[0]] = F[8,x,k[0]]*F[94,x,k[0]]
F[94,x,k[0]] = F[1,x]+F[92,x,k[0]]
F[95,x,k[0]] = F[34,x]+F[96,x,k[0]]+F[98,x,k[0]]
F[96,x,k[0]] = F[8,x,k[0]]*F[97,x,k[0]]
F[97,x,k[0]] = F[17,x]+F[95,x,k[0]]
F[98,x,k[0]] = F[11,x]*F[91,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]+F[103,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]*F[11,x]
F[102,x,k[0]] = F[100,x,k[0]]+F[92,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]*F[11,x]
F[105,x,k[0]] = F[103,x,k[0]]+F[95,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]+F[142,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]+F[121,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[11,x]*F[110,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]+F[114,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[92,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]
F[113,x,k[0]] = F[11,x]*F[92,x,k[0]]
F[114,x,k[0]] = F[108,x,k[0]]+F[115,x,k[0]]
F[115,x,k[0]] = 2*F[34,x]+F[116,x,k[0]]+F[120,x,k[0]]
F[116,x,k[0]] = F[11,x]*F[117,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]+F[119,x,k[0]]
F[118,x,k[0]] = F[112,x,k[0]]
F[119,x,k[0]] = F[115,x,k[0]]
F[120,x,k[0]] = F[108,x,k[0]]*F[11,x]
F[121,x,k[0]] = 2*F[34,x]+F[122,x,k[0]]+F[134,x,k[0]]
F[122,x,k[0]] = F[11,x]*F[123,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[95,x,k[0]]
F[125,x,k[0]] = F[126,x,k[0]]
F[126,x,k[0]] = F[11,x]*F[95,x,k[0]]
F[127,x,k[0]] = F[121,x,k[0]]+F[128,x,k[0]]
F[128,x,k[0]] = 3*F[34,x]+F[129,x,k[0]]+F[133,x,k[0]]
F[129,x,k[0]] = F[11,x]*F[130,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]+F[132,x,k[0]]
F[131,x,k[0]] = F[125,x,k[0]]
F[132,x,k[0]] = F[128,x,k[0]]
F[133,x,k[0]] = F[11,x]*F[121,x,k[0]]
F[134,x,k[0]] = F[11,x]*F[135,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]+F[139,x,k[0]]
F[136,x,k[0]] = F[137,x,k[0]]
F[137,x,k[0]] = F[11,x]*F[138,x,k[0]]
F[138,x,k[0]] = F[136,x,k[0]]+F[92,x,k[0]]
F[139,x,k[0]] = 2*F[34,x]+F[134,x,k[0]]+F[140,x,k[0]]
F[140,x,k[0]] = F[11,x]*F[141,x,k[0]]
F[141,x,k[0]] = F[139,x,k[0]]+F[95,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]+F[158,x,k[0]]
F[143,x,k[0]] = 2*F[34,x]+F[144,x,k[0]]+F[156,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[149,x,k[0]]
F[146,x,k[0]] = F[100,x,k[0]]+F[147,x,k[0]]
F[147,x,k[0]] = F[148,x,k[0]]
F[148,x,k[0]] = F[100,x,k[0]]*F[11,x]
F[149,x,k[0]] = F[143,x,k[0]]+F[150,x,k[0]]
F[150,x,k[0]] = 3*F[34,x]+F[151,x,k[0]]+F[155,x,k[0]]
F[151,x,k[0]] = F[11,x]*F[152,x,k[0]]
F[152,x,k[0]] = F[153,x,k[0]]+F[154,x,k[0]]
F[153,x,k[0]] = F[147,x,k[0]]
F[154,x,k[0]] = F[150,x,k[0]]
F[155,x,k[0]] = F[11,x]*F[143,x,k[0]]
F[156,x,k[0]] = F[11,x]*F[157,x,k[0]]
F[157,x,k[0]] = F[108,x,k[0]]+F[143,x,k[0]]
F[158,x,k[0]] = 3*F[34,x]+F[159,x,k[0]]+F[171,x,k[0]]
F[159,x,k[0]] = F[11,x]*F[160,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]+F[164,x,k[0]]
F[161,x,k[0]] = F[103,x,k[0]]+F[162,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]
F[163,x,k[0]] = F[103,x,k[0]]*F[11,x]
F[164,x,k[0]] = F[158,x,k[0]]+F[165,x,k[0]]
F[165,x,k[0]] = 4*F[34,x]+F[166,x,k[0]]+F[170,x,k[0]]
F[166,x,k[0]] = F[11,x]*F[167,x,k[0]]
F[167,x,k[0]] = F[168,x,k[0]]+F[169,x,k[0]]
F[168,x,k[0]] = F[162,x,k[0]]
F[169,x,k[0]] = F[165,x,k[0]]
F[170,x,k[0]] = F[11,x]*F[158,x,k[0]]
F[171,x,k[0]] = F[11,x]*F[172,x,k[0]]
F[172,x,k[0]] = F[121,x,k[0]]+F[158,x,k[0]]
F[173,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_{173}\! \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_{89}\! \left(x , y\right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{26}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{19}\! \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_{16}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{17}\! \left(x \right)+F_{23}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{58}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{40}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{32}\! \left(x \right) = F_{28}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)+F_{39}\! \left(x \right)
F_{34}\! \left(x \right) = 0
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_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{11}\! \left(x \right)
F_{38}\! \left(x \right) = F_{33}\! \left(x \right)
F_{39}\! \left(x \right) = F_{11}\! \left(x \right) F_{28}\! \left(x \right)
F_{40}\! \left(x \right) = F_{34}\! \left(x \right)+F_{41}\! \left(x \right)+F_{53}\! \left(x \right)
F_{41}\! \left(x \right) = F_{11}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{43}\! \left(x \right) = F_{17}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right)
F_{46}\! \left(x \right) = F_{40}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{48}\! \left(x \right)+F_{52}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{51}\! \left(x \right)
F_{50}\! \left(x \right) = F_{44}\! \left(x \right)
F_{51}\! \left(x \right) = F_{47}\! \left(x \right)
F_{52}\! \left(x \right) = F_{11}\! \left(x \right) F_{40}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{17}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{34}\! \left(x \right)+F_{53}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{11}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{17}\! \left(x \right)+F_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{74}\! \left(x \right)
F_{59}\! \left(x \right) = F_{34}\! \left(x \right)+F_{60}\! \left(x \right)+F_{72}\! \left(x \right)
F_{60}\! \left(x \right) = F_{11}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{65}\! \left(x \right)
F_{62}\! \left(x \right) = F_{20}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \left(x \right) F_{20}\! \left(x \right)
F_{65}\! \left(x \right) = F_{59}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{67}\! \left(x \right)+F_{71}\! \left(x \right)
F_{67}\! \left(x \right) = F_{11}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{63}\! \left(x \right)
F_{70}\! \left(x \right) = F_{66}\! \left(x \right)
F_{71}\! \left(x \right) = F_{11}\! \left(x \right) F_{59}\! \left(x \right)
F_{72}\! \left(x \right) = F_{11}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{28}\! \left(x \right)+F_{59}\! \left(x \right)
F_{74}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{75}\! \left(x \right)+F_{87}\! \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_{80}\! \left(x \right)
F_{77}\! \left(x \right) = F_{23}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{80}\! \left(x \right) = F_{74}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = 3 F_{34}\! \left(x \right)+F_{82}\! \left(x \right)+F_{86}\! \left(x \right)
F_{82}\! \left(x \right) = F_{11}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{78}\! \left(x \right)
F_{85}\! \left(x \right) = F_{81}\! \left(x \right)
F_{86}\! \left(x \right) = F_{11}\! \left(x \right) F_{74}\! \left(x \right)
F_{87}\! \left(x \right) = F_{11}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{40}\! \left(x \right)+F_{74}\! \left(x \right)
F_{89}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{92}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{34}\! \left(x \right)+F_{96}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{95}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{91}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{103}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{92}\! \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_{11}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{142}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{121}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{114}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = 2 F_{34}\! \left(x \right)+F_{116}\! \left(x , y\right)+F_{120}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{117}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{119}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{112}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{115}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{121}\! \left(x , y\right) = 2 F_{34}\! \left(x \right)+F_{122}\! \left(x , y\right)+F_{134}\! \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_{124}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = 3 F_{34}\! \left(x \right)+F_{129}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{130}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{132}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{128}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{121}\! \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_{136}\! \left(x , y\right)+F_{139}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{138}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = 2 F_{34}\! \left(x \right)+F_{134}\! \left(x , y\right)+F_{140}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{141}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{139}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right)+F_{158}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = 2 F_{34}\! \left(x \right)+F_{144}\! \left(x , y\right)+F_{156}\! \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_{149}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{149}\! \left(x , y\right) = F_{143}\! \left(x , y\right)+F_{150}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = 3 F_{34}\! \left(x \right)+F_{151}\! \left(x , y\right)+F_{155}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)+F_{154}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{150}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{143}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{157}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{143}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = 3 F_{34}\! \left(x \right)+F_{159}\! \left(x , y\right)+F_{171}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{160}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{164}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{164}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{165}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = 4 F_{34}\! \left(x \right)+F_{166}\! \left(x , y\right)+F_{170}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{167}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{169}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{162}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{165}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{158}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{172}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{158}\! \left(x , y\right)
F_{173}\! \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_173(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_89(x, k_0))
Eq(F_14(x), F_15(x) + F_26(x))
Eq(F_15(x), F_16(x) + F_19(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_16(x))
Eq(F_19(x), F_20(x) + F_23(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_11(x)*F_22(x))
Eq(F_22(x), F_1(x) + F_20(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_11(x)*F_25(x))
Eq(F_25(x), F_17(x) + F_23(x))
Eq(F_26(x), F_27(x) + F_58(x))
Eq(F_27(x), F_28(x) + F_40(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_11(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_1(x) + F_11(x))
Eq(F_32(x), F_28(x) + F_33(x))
Eq(F_33(x), F_34(x) + F_35(x) + F_39(x))
Eq(F_34(x), 0)
Eq(F_35(x), F_11(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_11(x))
Eq(F_38(x), F_33(x))
Eq(F_39(x), F_11(x)*F_28(x))
Eq(F_40(x), F_34(x) + F_41(x) + F_53(x))
Eq(F_41(x), F_11(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_46(x))
Eq(F_43(x), F_17(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_11(x)*F_17(x))
Eq(F_46(x), F_40(x) + F_47(x))
Eq(F_47(x), 2*F_34(x) + F_48(x) + F_52(x))
Eq(F_48(x), F_11(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_51(x))
Eq(F_50(x), F_44(x))
Eq(F_51(x), F_47(x))
Eq(F_52(x), F_11(x)*F_40(x))
Eq(F_53(x), F_11(x)*F_54(x))
Eq(F_54(x), F_17(x) + F_55(x))
Eq(F_55(x), F_34(x) + F_53(x) + F_56(x))
Eq(F_56(x), F_11(x)*F_57(x))
Eq(F_57(x), F_17(x) + F_55(x))
Eq(F_58(x), F_59(x) + F_74(x))
Eq(F_59(x), F_34(x) + F_60(x) + F_72(x))
Eq(F_60(x), F_11(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_65(x))
Eq(F_62(x), F_20(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_11(x)*F_20(x))
Eq(F_65(x), F_59(x) + F_66(x))
Eq(F_66(x), 2*F_34(x) + F_67(x) + F_71(x))
Eq(F_67(x), F_11(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_63(x))
Eq(F_70(x), F_66(x))
Eq(F_71(x), F_11(x)*F_59(x))
Eq(F_72(x), F_11(x)*F_73(x))
Eq(F_73(x), F_28(x) + F_59(x))
Eq(F_74(x), 2*F_34(x) + F_75(x) + F_87(x))
Eq(F_75(x), F_11(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_80(x))
Eq(F_77(x), F_23(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_11(x)*F_23(x))
Eq(F_80(x), F_74(x) + F_81(x))
Eq(F_81(x), 3*F_34(x) + F_82(x) + F_86(x))
Eq(F_82(x), F_11(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_78(x))
Eq(F_85(x), F_81(x))
Eq(F_86(x), F_11(x)*F_74(x))
Eq(F_87(x), F_11(x)*F_88(x))
Eq(F_88(x), F_40(x) + F_74(x))
Eq(F_89(x, k_0), F_106(x, k_0) + F_90(x, k_0))
Eq(F_90(x, k_0), F_91(x, k_0) + F_99(x, k_0))
Eq(F_91(x, k_0), F_92(x, k_0) + F_95(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0))
Eq(F_93(x, k_0), F_8(x, k_0)*F_94(x, k_0))
Eq(F_94(x, k_0), F_1(x) + F_92(x, k_0))
Eq(F_95(x, k_0), F_34(x) + F_96(x, k_0) + F_98(x, k_0))
Eq(F_96(x, k_0), F_8(x, k_0)*F_97(x, k_0))
Eq(F_97(x, k_0), F_17(x) + F_95(x, k_0))
Eq(F_98(x, k_0), F_11(x)*F_91(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + F_103(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0)*F_11(x))
Eq(F_102(x, k_0), F_100(x, k_0) + F_92(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_11(x))
Eq(F_105(x, k_0), F_103(x, k_0) + F_95(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0) + F_142(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0) + F_121(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_11(x)*F_110(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0) + F_114(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_92(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0))
Eq(F_113(x, k_0), F_11(x)*F_92(x, k_0))
Eq(F_114(x, k_0), F_108(x, k_0) + F_115(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0) + F_120(x, k_0) + 2*F_34(x))
Eq(F_116(x, k_0), F_11(x)*F_117(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0) + F_119(x, k_0))
Eq(F_118(x, k_0), F_112(x, k_0))
Eq(F_119(x, k_0), F_115(x, k_0))
Eq(F_120(x, k_0), F_108(x, k_0)*F_11(x))
Eq(F_121(x, k_0), F_122(x, k_0) + F_134(x, k_0) + 2*F_34(x))
Eq(F_122(x, k_0), F_11(x)*F_123(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) + F_95(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0))
Eq(F_126(x, k_0), F_11(x)*F_95(x, k_0))
Eq(F_127(x, k_0), F_121(x, k_0) + F_128(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0) + F_133(x, k_0) + 3*F_34(x))
Eq(F_129(x, k_0), F_11(x)*F_130(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0) + F_132(x, k_0))
Eq(F_131(x, k_0), F_125(x, k_0))
Eq(F_132(x, k_0), F_128(x, k_0))
Eq(F_133(x, k_0), F_11(x)*F_121(x, k_0))
Eq(F_134(x, k_0), F_11(x)*F_135(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0) + F_139(x, k_0))
Eq(F_136(x, k_0), F_137(x, k_0))
Eq(F_137(x, k_0), F_11(x)*F_138(x, k_0))
Eq(F_138(x, k_0), F_136(x, k_0) + F_92(x, k_0))
Eq(F_139(x, k_0), F_134(x, k_0) + F_140(x, k_0) + 2*F_34(x))
Eq(F_140(x, k_0), F_11(x)*F_141(x, k_0))
Eq(F_141(x, k_0), F_139(x, k_0) + F_95(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0) + F_158(x, k_0))
Eq(F_143(x, k_0), F_144(x, k_0) + F_156(x, k_0) + 2*F_34(x))
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_149(x, k_0))
Eq(F_146(x, k_0), F_100(x, k_0) + F_147(x, k_0))
Eq(F_147(x, k_0), F_148(x, k_0))
Eq(F_148(x, k_0), F_100(x, k_0)*F_11(x))
Eq(F_149(x, k_0), F_143(x, k_0) + F_150(x, k_0))
Eq(F_150(x, k_0), F_151(x, k_0) + F_155(x, k_0) + 3*F_34(x))
Eq(F_151(x, k_0), F_11(x)*F_152(x, k_0))
Eq(F_152(x, k_0), F_153(x, k_0) + F_154(x, k_0))
Eq(F_153(x, k_0), F_147(x, k_0))
Eq(F_154(x, k_0), F_150(x, k_0))
Eq(F_155(x, k_0), F_11(x)*F_143(x, k_0))
Eq(F_156(x, k_0), F_11(x)*F_157(x, k_0))
Eq(F_157(x, k_0), F_108(x, k_0) + F_143(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0) + F_171(x, k_0) + 3*F_34(x))
Eq(F_159(x, k_0), F_11(x)*F_160(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0) + F_164(x, k_0))
Eq(F_161(x, k_0), F_103(x, k_0) + F_162(x, k_0))
Eq(F_162(x, k_0), F_163(x, k_0))
Eq(F_163(x, k_0), F_103(x, k_0)*F_11(x))
Eq(F_164(x, k_0), F_158(x, k_0) + F_165(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0) + F_170(x, k_0) + 4*F_34(x))
Eq(F_166(x, k_0), F_11(x)*F_167(x, k_0))
Eq(F_167(x, k_0), F_168(x, k_0) + F_169(x, k_0))
Eq(F_168(x, k_0), F_162(x, k_0))
Eq(F_169(x, k_0), F_165(x, k_0))
Eq(F_170(x, k_0), F_11(x)*F_158(x, k_0))
Eq(F_171(x, k_0), F_11(x)*F_172(x, k_0))
Eq(F_172(x, k_0), F_121(x, k_0) + F_158(x, k_0))
Eq(F_173(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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "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": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "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"}}, {"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], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 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": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 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": [[0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 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": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 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": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 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": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 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": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 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}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": 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