0123_0132_1023_1230_3012
Counting sequence:
1, 1, 2, 6, 19, 59, 177, 531, 1640, 5270, 17564, 60213, 210663, 747863, 2683839, 9712865, 35392606, 129713144, 477773374, 1767529871, 6564650349, 24467322529, 91484669225, 343063818116, 1289912548074, 4861963193064, 18367386643532, 69533618044691, 263748085991135, 1002242485113471, 3814987038993867, 14544637113003821, 55534067024571834, 212336134707255788, 812944050739716658, 3116285512087228227, 11959798420220256713, 45950804393341291653, 176733862924445735789, 680425372004853797316, 2622127042826248022494, 10113918592737409872164, 39044429914103467336560, 150853479209483398305831, 583300119601792786257435, 2257117854094840259459427, 8740328711568357762311535, 33868773757261415630799662, 131327898242310102966556940, 509552245179898613031547270, 1978261657756723603577443314, 7684785670515442285137927053, 29869166945774877749956393033, 116157871455786937850181529973, 451959718027962478646864588713, 1759414616608836885390989722382, 6852456927844909526346677820318, 26700952856774923961839259261788, 104088460289122448148686395119884, 405944995127577273961019595563183, 1583850964596120619147525082980815, 6182127958584856803408585454617615, 24139737743045629131554467760559267, 94295850558771984399621403374399621, 368479169875816668702381079568995890, 1440418573150919687319233967954133652, 5632681584560312771887403853269010650, 22033725021956517537145528908895966507, 86218923998960285873759593253378381505, 337485502510215975851931698634412362893, 1321422108420282271080237987548936163253, 5175569924646105560599531814712478043732, 20276890389709399865290181809689464716006, 79463489365077377845930604115218915243708, 311496878311103321146981024484548425664824, 1221395654430378811847650187939440712923375, 4790408930363303911366165140257821624081811, 18793142726809884575286919142813459518089899, 73745243611532458459841267582099157887670519, 289450081175264899454586077484394424559644346, 1136359577947336271932237339914474771256624604, 4462290049988320482464450223325747812676103654, 17526585015616776834737558369554884894747477770, 68854441132780194707892887737947105659685953661, 270557451039395118028652134695725483454070947825, 1063353702922273835973056000856590292789900819917, 4180080073556524734514734513797135126562344130705, 16435314834665426797069222332015341479634773914782, 64633260585762914370496792228651092135215900085670, 254224158304000796523953750263851468431616099355188, 1000134600800354781929399869506561507052598542177748, 3935312233584004685417854810703388795154306581934167, 15487357822491889407128329439658421802774480928995591, 60960876535340415751462568532589806033490828506976023, 239993345518077005168915786526997037289323026684398379, 944973797977428207852605890261980225403315156624204850, 3721443204405954385563870580993327916841675494154125376, 14657929356129575437016877925885195275977292544447308594, 57743358069601357782187700766499181362549406811848266734, 227508830794229349661819540712601504013099032975720760401, 896519947090131496687170070707925932534952222287101585229
Generating function in Maple syntax:
1/2*(-2*(x-1/2)*(x-1)^5*(1-4*x)^(1/2)+4*x^8-8*x^7+6*x^6-15*x^5+27*x^4-30*x^3+20*x^2-7*x+1)/x/(2*x-1)/(x-1)^5
Generating function in latex syntax:
\frac{-2 \left(x -\frac{1}{2}\right) \left(x -1\right)^{5} \sqrt{1-4 x}+4 x^{8}-8 x^{7}+6 x^{6}-15 x^{5}+27 x^{4}-30 x^{3}+20 x^{2}-7 x +1}{2 x \left(2 x -1\right) \left(x -1\right)^{5}}
Generating function in sympy syntax:
(2*x**8 - 4*x**7 + 3*x**6 - 15*x**5/2 + 27*x**4/2 - 15*x**3 + 10*x**2 - 7*x/2 + sqrt(1 - 4*x)*(1 - 2*x)*(x - 1)**5/2 + 1/2)/(x*(x - 1)**5*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*(x-1)^10*F(x)^2-(2*x-1)*(4*x^8-8*x^7+6*x^6-15*x^5+27*x^4-30*x^3+20*x^2-7*x+1)*(x-1)^5*F(x)+4*x^15-16*x^14+28*x^13-50*x^12+78*x^11+19*x^10-428*x^9+1146*x^8-1812*x^7+1970*x^6-1536*x^5+861*x^4-339*x^3+89*x^2-14*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} \left(x -1\right)^{10} F \! \left(x \right)^{2}-\left(2 x -1\right) \left(4 x^{8}-8 x^{7}+6 x^{6}-15 x^{5}+27 x^{4}-30 x^{3}+20 x^{2}-7 x +1\right) \left(x -1\right)^{5} F \! \left(x \right)+4 x^{15}-16 x^{14}+28 x^{13}-50 x^{12}+78 x^{11}+19 x^{10}-428 x^{9}+1146 x^{8}-1812 x^{7}+1970 x^{6}-1536 x^{5}+861 x^{4}-339 x^{3}+89 x^{2}-14 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 59
a(6) = 177
a(7) = 531
a(8) = 1640
a(9) = 5270
a(10) = 17564
a(n+3) = 8*(2*n+1)/(n+4)*a(n)-4*(5*n+8)/(n+4)*a(n+1)+2*(4*n+11)/(n+4)*a(n+2)-1/24*n*(3*n^4-40*n^3-3*n^2+892*n-1308)/(n+4), n >= 11
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) = 19
a \! \left(5\right) = 59
a \! \left(6\right) = 177
a \! \left(7\right) = 531
a \! \left(8\right) = 1640
a \! \left(9\right) = 5270
a \! \left(10\right) = 17564
a \! \left(n +3\right) = \frac{8 \left(2 n +1\right) a \! \left(n \right)}{n +4}-\frac{4 \left(5 n +8\right) a \! \left(n +1\right)}{n +4}+\frac{2 \left(4 n +11\right) a \! \left(n +2\right)}{n +4}-\frac{n \left(3 n^{4}-40 n^{3}-3 n^{2}+892 n -1308\right)}{24 \left(n +4\right)}, \quad n \geq 11
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21509/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[12,x]*F[3,x]
F[3,x] = F[1,x]+F[111,x]+F[4,x]
F[4,x] = F[12,x]*F[5,x]
F[5,x] = F[1,x]+F[110,x]+F[49,x]+F[6,x]
F[6,x] = F[12,x]*F[7,x]
F[7,x] = F[22,x]+F[8,x]
F[8,x] = F[14,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = F[13,x,1]
F[13,x,k[0]] = k[0]*x
F[14,x] = F[10,x]+F[15,x]
F[15,x] = F[16,x]+F[17,x]+F[21,x]
F[16,x] = 0
F[17,x] = F[12,x]*F[18,x]
F[18,x] = F[12,x]+F[19,x]
F[19,x] = F[16,x]+F[17,x]+F[20,x]
F[20,x] = F[10,x]*F[12,x]
F[21,x] = F[12,x]*F[14,x]
F[22,x] = F[23,x]+F[28,x]
F[23,x] = F[10,x]+F[24,x]
F[24,x] = F[16,x]+F[25,x]+F[27,x]
F[25,x] = F[12,x]*F[26,x]
F[26,x] = F[10,x]+F[24,x]
F[27,x] = F[12,x]*F[23,x]
F[28,x] = F[24,x]+F[29,x]
F[29,x] = F[16,x]+F[30,x]+F[38,x]+F[48,x]
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[32,x]+F[35,x]
F[32,x] = F[33,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[10,x]+F[32,x]
F[35,x] = 2*F[16,x]+F[30,x]+F[36,x]
F[36,x] = F[12,x]*F[37,x]
F[37,x] = F[24,x]+F[35,x]
F[38,x] = F[12,x]*F[39,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[41,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[12,x]+F[40,x]
F[43,x] = 2*F[16,x]+F[38,x]+F[44,x]
F[44,x] = F[12,x]*F[45,x]
F[45,x] = F[46,x]+F[47,x]
F[46,x] = F[20,x]
F[47,x] = F[44,x]
F[48,x] = F[12,x]*F[28,x]
F[49,x] = F[12,x]*F[50,x]
F[50,x] = F[51,x,1]
F[51,x,k[0]] = F[1,x]+F[100,x,k[0]]+F[108,x,k[0]]+F[52,x,k[0]]+F[98,x,k[0]]
F[52,x,k[0]] = F[12,x]*F[53,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]+F[69,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]+F[62,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]+F[9,x]
F[56,x,k[0]] = F[57,x,k[0]]+F[60,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[58,x,k[0]] = F[13,x,k[0]]*F[59,x,k[0]]
F[59,x,k[0]] = F[1,x]+F[57,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[12,x]*F[56,x,k[0]]
F[62,x,k[0]] = F[14,x]+F[63,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]+F[67,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[13,x,k[0]]*F[66,x,k[0]]
F[66,x,k[0]] = F[10,x]+F[64,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[12,x]*F[63,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]+F[81,x,k[0]]
F[70,x,k[0]] = F[23,x]+F[71,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]+F[77,x,k[0]]
F[72,x,k[0]] = F[16,x]+F[73,x,k[0]]+F[75,x,k[0]]
F[73,x,k[0]] = F[12,x]*F[74,x,k[0]]
F[74,x,k[0]] = F[57,x,k[0]]+F[72,x,k[0]]
F[75,x,k[0]] = F[13,x,k[0]]*F[76,x,k[0]]
F[76,x,k[0]] = F[10,x]+F[72,x,k[0]]
F[77,x,k[0]] = 2*F[16,x]+F[78,x,k[0]]+F[80,x,k[0]]
F[78,x,k[0]] = F[12,x]*F[79,x,k[0]]
F[79,x,k[0]] = F[60,x,k[0]]+F[77,x,k[0]]
F[80,x,k[0]] = F[12,x]*F[71,x,k[0]]
F[81,x,k[0]] = F[28,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]] = 2*F[16,x]+F[84,x,k[0]]+F[86,x,k[0]]
F[84,x,k[0]] = F[12,x]*F[85,x,k[0]]
F[85,x,k[0]] = F[64,x,k[0]]+F[83,x,k[0]]
F[86,x,k[0]] = F[13,x,k[0]]*F[87,x,k[0]]
F[87,x,k[0]] = F[24,x]+F[83,x,k[0]]
F[88,x,k[0]] = 3*F[16,x]+F[89,x,k[0]]+F[97,x,k[0]]
F[89,x,k[0]] = F[12,x]*F[90,x,k[0]]
F[90,x,k[0]] = F[91,x,k[0]]+F[94,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]
F[92,x,k[0]] = F[12,x]*F[93,x,k[0]]
F[93,x,k[0]] = F[64,x,k[0]]+F[91,x,k[0]]
F[94,x,k[0]] = 3*F[16,x]+F[89,x,k[0]]+F[95,x,k[0]]
F[95,x,k[0]] = F[12,x]*F[96,x,k[0]]
F[96,x,k[0]] = F[83,x,k[0]]+F[94,x,k[0]]
F[97,x,k[0]] = F[12,x]*F[82,x,k[0]]
F[98,x,k[0]] = F[12,x]*F[99,x,k[0]]
F[99,x,k[0]] = 1/(-1+k[0])*(F[51,x,k[0]]*k[0]-F[51,x,1])
F[100,x,k[0]] = F[101,x,k[0]]*F[13,x,k[0]]
F[101,x,k[0]] = F[1,x]+F[100,x,k[0]]+F[102,x,k[0]]+F[106,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]*F[12,x]
F[103,x,k[0]] = F[104,x,k[0]]+F[105,x,k[0]]
F[104,x,k[0]] = F[59,x,k[0]]+F[66,x,k[0]]
F[105,x,k[0]] = F[76,x,k[0]]+F[87,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]*F[12,x]
F[107,x,k[0]] = 1/(-1+k[0])*(F[101,x,k[0]]*k[0]-F[101,x,1])
F[108,x,k[0]] = F[109,x,k[0]]*F[12,x]
F[109,x,k[0]] = 1/(-1+k[0])*(F[101,x,k[0]]*k[0]-F[101,x,1])
F[110,x] = F[100,x,1]
F[111,x] = F[112,x]*F[12,x]
F[112,x] = F[113,x]+F[138,x]
F[113,x] = F[114,x]+F[126,x]
F[114,x] = F[1,x]+F[115,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[12,x]
F[117,x] = F[118,x]+F[119,x]
F[118,x] = F[1,x]+F[12,x]
F[119,x] = F[115,x]+F[120,x]
F[120,x] = F[121,x]+F[125,x]+F[16,x]
F[121,x] = F[12,x]*F[122,x]
F[122,x] = F[123,x]+F[124,x]
F[123,x] = F[12,x]
F[124,x] = F[120,x]
F[125,x] = F[115,x]*F[12,x]
F[126,x] = F[10,x]+F[127,x]
F[127,x] = F[128,x]
F[128,x] = F[12,x]*F[129,x]
F[129,x] = F[130,x]+F[131,x]
F[130,x] = F[10,x]+F[46,x]
F[131,x] = F[127,x]+F[132,x]
F[132,x] = 2*F[16,x]+F[133,x]+F[137,x]
F[133,x] = F[12,x]*F[134,x]
F[134,x] = F[135,x]+F[136,x]
F[135,x] = F[46,x]
F[136,x] = F[132,x]
F[137,x] = F[12,x]*F[127,x]
F[138,x] = F[139,x]+F[166,x]
F[139,x] = F[140,x]+F[146,x]
F[140,x] = F[141,x]
F[141,x] = F[12,x]*F[142,x]
F[142,x] = F[143,x]+F[9,x]
F[143,x] = F[140,x]+F[144,x]
F[144,x] = F[145,x]
F[145,x] = F[12,x]*F[143,x]
F[146,x] = F[147,x]+F[156,x]+F[16,x]
F[147,x] = F[12,x]*F[148,x]
F[148,x] = F[149,x]+F[150,x]
F[149,x] = F[10,x]+F[32,x]
F[150,x] = F[151,x]+F[152,x]
F[151,x] = F[147,x]+F[16,x]+F[27,x]
F[152,x] = F[153,x]
F[153,x] = F[12,x]*F[154,x]
F[154,x] = F[155,x]+F[32,x]
F[155,x] = F[153,x]
F[156,x] = F[12,x]*F[157,x]
F[157,x] = F[158,x]+F[159,x]
F[158,x] = F[10,x]+F[40,x]
F[159,x] = F[160,x]+F[161,x]
F[160,x] = F[156,x]+F[16,x]+F[25,x]
F[161,x] = 2*F[16,x]+F[162,x]+F[44,x]
F[162,x] = F[12,x]*F[163,x]
F[163,x] = F[164,x]+F[165,x]
F[164,x] = F[40,x]
F[165,x] = F[161,x]
F[166,x] = F[144,x]+F[167,x]
F[167,x] = F[168,x]
F[168,x] = F[12,x]*F[169,x]
F[169,x] = F[170,x]+F[171,x]
F[170,x] = F[32,x]
F[171,x] = F[168,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_{12}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{111}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{12}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{110}\! \left(x \right)+F_{49}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{12}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{22}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{13}\! \left(x , y\right) = y x
F_{14}\! \left(x \right) = F_{10}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)+F_{21}\! \left(x \right)
F_{16}\! \left(x \right) = 0
F_{17}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{28}\! \left(x \right)
F_{23}\! \left(x \right) = F_{10}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{16}\! \left(x \right)+F_{25}\! \left(x \right)+F_{27}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{10}\! \left(x \right)+F_{24}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{28}\! \left(x \right) = F_{24}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{16}\! \left(x \right)+F_{30}\! \left(x \right)+F_{38}\! \left(x \right)+F_{48}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{10}\! \left(x \right)+F_{32}\! \left(x \right)
F_{35}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{30}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{24}\! \left(x \right)+F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right)+F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{38}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)
F_{46}\! \left(x \right) = F_{20}\! \left(x \right)
F_{47}\! \left(x \right) = F_{44}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x , 1\right)
F_{51}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{108}\! \left(x , y\right)+F_{52}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{9}\! \left(x \right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{57}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{64}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{16}\! \left(x \right)+F_{73}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = 2 F_{16}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{28}\! \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) = 2 F_{16}\! \left(x \right)+F_{84}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = 3 F_{16}\! \left(x \right)+F_{89}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = 3 F_{16}\! \left(x \right)+F_{89}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = -\frac{-y F_{51}\! \left(x , y\right)+F_{51}\! \left(x , 1\right)}{-1+y}
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{13}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{102}\! \left(x , y\right)+F_{106}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{105}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{107}\! \left(x , y\right) = -\frac{-y F_{101}\! \left(x , y\right)+F_{101}\! \left(x , 1\right)}{-1+y}
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{109}\! \left(x , y\right) = -\frac{-y F_{101}\! \left(x , y\right)+F_{101}\! \left(x , 1\right)}{-1+y}
F_{110}\! \left(x \right) = F_{100}\! \left(x , 1\right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{12}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{138}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{126}\! \left(x \right)
F_{114}\! \left(x \right) = F_{1}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{12}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{119}\! \left(x \right)
F_{118}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{119}\! \left(x \right) = F_{115}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{125}\! \left(x \right)+F_{16}\! \left(x \right)
F_{121}\! \left(x \right) = F_{12}\! \left(x \right) F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{124}\! \left(x \right)
F_{123}\! \left(x \right) = F_{12}\! \left(x \right)
F_{124}\! \left(x \right) = F_{120}\! \left(x \right)
F_{125}\! \left(x \right) = F_{115}\! \left(x \right) F_{12}\! \left(x \right)
F_{126}\! \left(x \right) = F_{10}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{12}\! \left(x \right) F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{131}\! \left(x \right)
F_{130}\! \left(x \right) = F_{10}\! \left(x \right)+F_{46}\! \left(x \right)
F_{131}\! \left(x \right) = F_{127}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{133}\! \left(x \right)+F_{137}\! \left(x \right)
F_{133}\! \left(x \right) = F_{12}\! \left(x \right) F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{136}\! \left(x \right)
F_{135}\! \left(x \right) = F_{46}\! \left(x \right)
F_{136}\! \left(x \right) = F_{132}\! \left(x \right)
F_{137}\! \left(x \right) = F_{12}\! \left(x \right) F_{127}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{166}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{146}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{12}\! \left(x \right) F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{9}\! \left(x \right)
F_{143}\! \left(x \right) = F_{140}\! \left(x \right)+F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{12}\! \left(x \right) F_{143}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{156}\! \left(x \right)+F_{16}\! \left(x \right)
F_{147}\! \left(x \right) = F_{12}\! \left(x \right) F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{150}\! \left(x \right)
F_{149}\! \left(x \right) = F_{10}\! \left(x \right)+F_{32}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{152}\! \left(x \right)
F_{151}\! \left(x \right) = F_{147}\! \left(x \right)+F_{16}\! \left(x \right)+F_{27}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{12}\! \left(x \right) F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{32}\! \left(x \right)
F_{155}\! \left(x \right) = F_{153}\! \left(x \right)
F_{156}\! \left(x \right) = F_{12}\! \left(x \right) F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{159}\! \left(x \right)
F_{158}\! \left(x \right) = F_{10}\! \left(x \right)+F_{40}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{161}\! \left(x \right)
F_{160}\! \left(x \right) = F_{156}\! \left(x \right)+F_{16}\! \left(x \right)+F_{25}\! \left(x \right)
F_{161}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{162}\! \left(x \right)+F_{44}\! \left(x \right)
F_{162}\! \left(x \right) = F_{12}\! \left(x \right) F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)+F_{165}\! \left(x \right)
F_{164}\! \left(x \right) = F_{40}\! \left(x \right)
F_{165}\! \left(x \right) = F_{161}\! \left(x \right)
F_{166}\! \left(x \right) = F_{144}\! \left(x \right)+F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{12}\! \left(x \right) F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)+F_{171}\! \left(x \right)
F_{170}\! \left(x \right) = F_{32}\! \left(x \right)
F_{171}\! \left(x \right) = F_{168}\! \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_12(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_111(x) + F_4(x))
Eq(F_4(x), F_12(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_110(x) + F_49(x) + F_6(x))
Eq(F_6(x), F_12(x)*F_7(x))
Eq(F_7(x), F_22(x) + F_8(x))
Eq(F_8(x), F_14(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), F_13(x, 1))
Eq(F_13(x, k_0), k_0*x)
Eq(F_14(x), F_10(x) + F_15(x))
Eq(F_15(x), F_16(x) + F_17(x) + F_21(x))
Eq(F_16(x), 0)
Eq(F_17(x), F_12(x)*F_18(x))
Eq(F_18(x), F_12(x) + F_19(x))
Eq(F_19(x), F_16(x) + F_17(x) + F_20(x))
Eq(F_20(x), F_10(x)*F_12(x))
Eq(F_21(x), F_12(x)*F_14(x))
Eq(F_22(x), F_23(x) + F_28(x))
Eq(F_23(x), F_10(x) + F_24(x))
Eq(F_24(x), F_16(x) + F_25(x) + F_27(x))
Eq(F_25(x), F_12(x)*F_26(x))
Eq(F_26(x), F_10(x) + F_24(x))
Eq(F_27(x), F_12(x)*F_23(x))
Eq(F_28(x), F_24(x) + F_29(x))
Eq(F_29(x), F_16(x) + F_30(x) + F_38(x) + F_48(x))
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_35(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_10(x) + F_32(x))
Eq(F_35(x), 2*F_16(x) + F_30(x) + F_36(x))
Eq(F_36(x), F_12(x)*F_37(x))
Eq(F_37(x), F_24(x) + F_35(x))
Eq(F_38(x), F_12(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_12(x) + F_40(x))
Eq(F_43(x), 2*F_16(x) + F_38(x) + F_44(x))
Eq(F_44(x), F_12(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_47(x))
Eq(F_46(x), F_20(x))
Eq(F_47(x), F_44(x))
Eq(F_48(x), F_12(x)*F_28(x))
Eq(F_49(x), F_12(x)*F_50(x))
Eq(F_50(x), F_51(x, 1))
Eq(F_51(x, k_0), F_1(x) + F_100(x, k_0) + F_108(x, k_0) + F_52(x, k_0) + F_98(x, k_0))
Eq(F_52(x, k_0), F_12(x)*F_53(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0) + F_69(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0) + F_62(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0) + F_9(x))
Eq(F_56(x, k_0), F_57(x, k_0) + F_60(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_58(x, k_0), F_13(x, k_0)*F_59(x, k_0))
Eq(F_59(x, k_0), F_1(x) + F_57(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_12(x)*F_56(x, k_0))
Eq(F_62(x, k_0), F_14(x) + F_63(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0) + F_67(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_13(x, k_0)*F_66(x, k_0))
Eq(F_66(x, k_0), F_10(x) + F_64(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_12(x)*F_63(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0) + F_81(x, k_0))
Eq(F_70(x, k_0), F_23(x) + F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0) + F_77(x, k_0))
Eq(F_72(x, k_0), F_16(x) + F_73(x, k_0) + F_75(x, k_0))
Eq(F_73(x, k_0), F_12(x)*F_74(x, k_0))
Eq(F_74(x, k_0), F_57(x, k_0) + F_72(x, k_0))
Eq(F_75(x, k_0), F_13(x, k_0)*F_76(x, k_0))
Eq(F_76(x, k_0), F_10(x) + F_72(x, k_0))
Eq(F_77(x, k_0), 2*F_16(x) + F_78(x, k_0) + F_80(x, k_0))
Eq(F_78(x, k_0), F_12(x)*F_79(x, k_0))
Eq(F_79(x, k_0), F_60(x, k_0) + F_77(x, k_0))
Eq(F_80(x, k_0), F_12(x)*F_71(x, k_0))
Eq(F_81(x, k_0), F_28(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), 2*F_16(x) + F_84(x, k_0) + F_86(x, k_0))
Eq(F_84(x, k_0), F_12(x)*F_85(x, k_0))
Eq(F_85(x, k_0), F_64(x, k_0) + F_83(x, k_0))
Eq(F_86(x, k_0), F_13(x, k_0)*F_87(x, k_0))
Eq(F_87(x, k_0), F_24(x) + F_83(x, k_0))
Eq(F_88(x, k_0), 3*F_16(x) + F_89(x, k_0) + F_97(x, k_0))
Eq(F_89(x, k_0), F_12(x)*F_90(x, k_0))
Eq(F_90(x, k_0), F_91(x, k_0) + F_94(x, k_0))
Eq(F_91(x, k_0), F_92(x, k_0))
Eq(F_92(x, k_0), F_12(x)*F_93(x, k_0))
Eq(F_93(x, k_0), F_64(x, k_0) + F_91(x, k_0))
Eq(F_94(x, k_0), 3*F_16(x) + F_89(x, k_0) + F_95(x, k_0))
Eq(F_95(x, k_0), F_12(x)*F_96(x, k_0))
Eq(F_96(x, k_0), F_83(x, k_0) + F_94(x, k_0))
Eq(F_97(x, k_0), F_12(x)*F_82(x, k_0))
Eq(F_98(x, k_0), F_12(x)*F_99(x, k_0))
Eq(F_99(x, k_0), (k_0*F_51(x, k_0) - F_51(x, 1))/(k_0 - 1))
Eq(F_100(x, k_0), F_101(x, k_0)*F_13(x, k_0))
Eq(F_101(x, k_0), F_1(x) + F_100(x, k_0) + F_102(x, k_0) + F_106(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0)*F_12(x))
Eq(F_103(x, k_0), F_104(x, k_0) + F_105(x, k_0))
Eq(F_104(x, k_0), F_59(x, k_0) + F_66(x, k_0))
Eq(F_105(x, k_0), F_76(x, k_0) + F_87(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0)*F_12(x))
Eq(F_107(x, k_0), (k_0*F_101(x, k_0) - F_101(x, 1))/(k_0 - 1))
Eq(F_108(x, k_0), F_109(x, k_0)*F_12(x))
Eq(F_109(x, k_0), (-k_0*F_101(x, k_0) + F_101(x, 1))/(1 - k_0))
Eq(F_110(x), F_100(x, 1))
Eq(F_111(x), F_112(x)*F_12(x))
Eq(F_112(x), F_113(x) + F_138(x))
Eq(F_113(x), F_114(x) + F_126(x))
Eq(F_114(x), F_1(x) + F_115(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_12(x))
Eq(F_117(x), F_118(x) + F_119(x))
Eq(F_118(x), F_1(x) + F_12(x))
Eq(F_119(x), F_115(x) + F_120(x))
Eq(F_120(x), F_121(x) + F_125(x) + F_16(x))
Eq(F_121(x), F_12(x)*F_122(x))
Eq(F_122(x), F_123(x) + F_124(x))
Eq(F_123(x), F_12(x))
Eq(F_124(x), F_120(x))
Eq(F_125(x), F_115(x)*F_12(x))
Eq(F_126(x), F_10(x) + F_127(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_12(x)*F_129(x))
Eq(F_129(x), F_130(x) + F_131(x))
Eq(F_130(x), F_10(x) + F_46(x))
Eq(F_131(x), F_127(x) + F_132(x))
Eq(F_132(x), F_133(x) + F_137(x) + 2*F_16(x))
Eq(F_133(x), F_12(x)*F_134(x))
Eq(F_134(x), F_135(x) + F_136(x))
Eq(F_135(x), F_46(x))
Eq(F_136(x), F_132(x))
Eq(F_137(x), F_12(x)*F_127(x))
Eq(F_138(x), F_139(x) + F_166(x))
Eq(F_139(x), F_140(x) + F_146(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_12(x)*F_142(x))
Eq(F_142(x), F_143(x) + F_9(x))
Eq(F_143(x), F_140(x) + F_144(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_12(x)*F_143(x))
Eq(F_146(x), F_147(x) + F_156(x) + F_16(x))
Eq(F_147(x), F_12(x)*F_148(x))
Eq(F_148(x), F_149(x) + F_150(x))
Eq(F_149(x), F_10(x) + F_32(x))
Eq(F_150(x), F_151(x) + F_152(x))
Eq(F_151(x), F_147(x) + F_16(x) + F_27(x))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_12(x)*F_154(x))
Eq(F_154(x), F_155(x) + F_32(x))
Eq(F_155(x), F_153(x))
Eq(F_156(x), F_12(x)*F_157(x))
Eq(F_157(x), F_158(x) + F_159(x))
Eq(F_158(x), F_10(x) + F_40(x))
Eq(F_159(x), F_160(x) + F_161(x))
Eq(F_160(x), F_156(x) + F_16(x) + F_25(x))
Eq(F_161(x), 2*F_16(x) + F_162(x) + F_44(x))
Eq(F_162(x), F_12(x)*F_163(x))
Eq(F_163(x), F_164(x) + F_165(x))
Eq(F_164(x), F_40(x))
Eq(F_165(x), F_161(x))
Eq(F_166(x), F_144(x) + F_167(x))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_12(x)*F_169(x))
Eq(F_169(x), F_170(x) + F_171(x))
Eq(F_170(x), F_32(x))
Eq(F_171(x), F_168(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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "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], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "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], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 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], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 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, 1, 3, 2], "pos": [[0, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 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"}}, {"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], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}], "requirements": []}, {"assumptions": [], "class_module": 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