0132_0213_1023_1230_3012
Counting sequence:
1, 1, 2, 6, 19, 55, 159, 479, 1515, 4999, 17009, 59110, 208499, 743629, 2675533, 9696493, 35360175, 129648633, 477644651, 1767272486, 6564135053, 24466290203, 91482600561, 343059672692, 1289904242039, 4861946553755, 18367353317489, 69533551311714, 263747952389205, 1002242217683425, 3814986503760387, 14544636041923883, 55534064881409715, 212336130419297659, 812944042161142457, 3116285494925762670, 11959798385890321267, 45950804324670065697, 176733862787084886101, 680425371730102301426, 2622127042276696786933, 10113918591638229304883, 39044429911904979799231, 150853479205086218661832, 583300119592998095918665, 2257117854077250343074163, 8740328711533177062685217, 33868773757191052828875760, 131327898242169375093063055, 509552245179617153612110999, 1978261657756160678796332009, 7684785670514316425960859030, 29869166945772626016044999709, 116157871455782434357186451549, 451959718027953471620144676667, 1759414616608818871271647626990, 6852456927844873498001361359357, 26700952856774851904976091534137, 104088460289122304034680892302581, 405944995127576985732556887451588, 1583850964596120042689868796584839, 6182127958584855650492090308816129, 24139737743045626825719564025386773, 94295850558771979787948499887059397, 368479169875816659479030263133303935, 1440418573150919668872524229604264033, 5632681584560312734993971261629261307, 22033725021956517463358642505197423430, 86218923998960285726185786110621654765, 337485502510215975556784028793119598947, 1321422108420282270489942557975211017473, 5175569924646105559418940810118108113624, 20276890389709399862928999565162664843727, 79463489365077377841208239245380335045339, 311496878311103321137536294128748223949233, 1221395654430378811828760726230932286814498, 4790408930363303911328386215227773706908085, 18793142726809884575211361290143424595092553, 73745243611532458459690151872536117886994451, 289450081175264899454283846058435435313823596, 1136359577947336271931632877051500913364631313, 4462290049988320482463241297581911308246027713, 17526585015616776834735140518038267217839545861, 68854441132780194707888052034867036849174808812, 270557451039395118028642463289489567708304109735, 1063353702922273835973036658043995849716925748293, 4180080073556524734514695828171747850710206395837, 16435314834665426797069144960764245926642867725280, 64633260585762914370496637486148381638238267574425, 254224158304000796523953440778845207045379381568367, 1000134600800354781929399250536547624496849831700343, 3935312233584004685417853572763358829867252431205724, 15487357822491889407128326963778358312241540620653857, 60960876535340415751462563580829673292290559151321059, 239993345518077005168915776623476762486829267224809793, 944973797977428207852605870454939660718100028215242088, 3721443204405954385563870541379246763070924407095483135, 14657929356129575437016877846657032928955241930596748303, 57743358069601357782187700608042856604624436314170255001, 227508830794229349661819540395688854393887674270651542046, 896519947090131496687170070074100633129287217897269900973
Generating function in Maple syntax:
1/2*(-(x^2+x-1)*(x-1)^4*(1-4*x)^(1/2)-2*x^10+4*x^9-2*x^8-2*x^7+7*x^6-3*x^5-x^4+6*x^3-9*x^2+5*x-1)/x/(x^2+x-1)/(x-1)^4
Generating function in latex syntax:
\frac{-\left(x^{2}+x -1\right) \left(x -1\right)^{4} \sqrt{1-4 x}-2 x^{10}+4 x^{9}-2 x^{8}-2 x^{7}+7 x^{6}-3 x^{5}-x^{4}+6 x^{3}-9 x^{2}+5 x -1}{2 x \left(x^{2}+x -1\right) \left(x -1\right)^{4}}
Generating function in sympy syntax:
(-x**10 + 2*x**9 - x**8 - x**7 + 7*x**6/2 - 3*x**5/2 - x**4/2 + 3*x**3 - 9*x**2/2 + 5*x/2 + sqrt(1 - 4*x)*(x - 1)**4*(-x**2 - x + 1)/2 - 1/2)/(x*(x - 1)**4*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
x*(x^2+x-1)^2*(x-1)^8*F(x)^2+(x^2+x-1)*(2*x^10-4*x^9+2*x^8+2*x^7-7*x^6+3*x^5+x^4-6*x^3+9*x^2-5*x+1)*(x-1)^4*F(x)+x^19-4*x^18+6*x^17-2*x^16-10*x^15+19*x^14-11*x^13-11*x^12+31*x^11-26*x^10+16*x^9-30*x^8+45*x^7-4*x^6-86*x^5+134*x^4-101*x^3+43*x^2-10*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(x^{2}+x -1\right)^{2} \left(x -1\right)^{8} F \! \left(x \right)^{2}+\left(x^{2}+x -1\right) \left(2 x^{10}-4 x^{9}+2 x^{8}+2 x^{7}-7 x^{6}+3 x^{5}+x^{4}-6 x^{3}+9 x^{2}-5 x +1\right) \left(x -1\right)^{4} F \! \left(x \right)+x^{19}-4 x^{18}+6 x^{17}-2 x^{16}-10 x^{15}+19 x^{14}-11 x^{13}-11 x^{12}+31 x^{11}-26 x^{10}+16 x^{9}-30 x^{8}+45 x^{7}-4 x^{6}-86 x^{5}+134 x^{4}-101 x^{3}+43 x^{2}-10 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 55
a(6) = 159
a(7) = 479
a(8) = 1515
a(9) = 4999
a(10) = 17009
a(11) = 59110
a(12) = 208499
a(13) = 743629
a(n+5) = 2*(2*n+1)/(6+n)*a(n)+(7*n+10)/(6+n)*a(1+n)-2*(3*n+8)/(6+n)*a(n+2)-(24+7*n)/(6+n)*a(n+3)+2*(3*n+14)/(6+n)*a(n+4)-1/2*(n^4-12*n^3-11*n^2+132*n+68)/(6+n), n >= 14
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 55
a \! \left(6\right) = 159
a \! \left(7\right) = 479
a \! \left(8\right) = 1515
a \! \left(9\right) = 4999
a \! \left(10\right) = 17009
a \! \left(11\right) = 59110
a \! \left(12\right) = 208499
a \! \left(13\right) = 743629
a \! \left(n +5\right) = \frac{2 \left(2 n +1\right) a \! \left(n \right)}{6+n}+\frac{\left(7 n +10\right) a \! \left(1+n \right)}{6+n}-\frac{2 \left(3 n +8\right) a \! \left(n +2\right)}{6+n}-\frac{\left(24+7 n \right) a \! \left(n +3\right)}{6+n}+\frac{2 \left(3 n +14\right) a \! \left(n +4\right)}{6+n}-\frac{n^{4}-12 n^{3}-11 n^{2}+132 n +68}{2 \left(6+n \right)}, \quad n \geq 14
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21610/
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[4,x]+F[77,x]
F[4,x] = F[12,x]*F[5,x]
F[5,x] = F[30,x]+F[6,x]
F[6,x] = F[16,x]+F[7,x]
F[7,x] = F[1,x]+F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[12,x]
F[10,x] = F[11,x]+F[13,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = x
F[13,x] = F[14,x]+F[8,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[8,x]
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[19,x]
F[19,x] = F[1,x]+F[17,x]
F[20,x] = F[21,x]
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[12,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = x^2
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[21,x]
F[28,x] = F[29,x]
F[29,x] = F[12,x]*F[27,x]
F[30,x] = F[31,x]+F[68,x]
F[31,x] = F[32,x]+F[8,x]
F[32,x] = F[33,x]+F[34,x]+F[56,x]
F[33,x] = 0
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[36,x]+F[43,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[38,x]
F[38,x] = F[12,x]*F[39,x]
F[39,x] = F[1,x]+F[37,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] = F[44,x]+F[50,x]
F[44,x] = F[33,x]+F[34,x]+F[45,x]
F[45,x] = F[12,x]*F[46,x]
F[46,x] = F[37,x]+F[47,x]
F[47,x] = F[33,x]+F[45,x]+F[48,x]
F[48,x] = F[12,x]*F[49,x]
F[49,x] = F[37,x]+F[47,x]
F[50,x] = F[51,x]
F[51,x] = F[12,x]*F[52,x]
F[52,x] = F[53,x]+F[55,x]
F[53,x] = F[54,x]
F[54,x] = F[12,x]*F[37,x]
F[55,x] = F[51,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[58,x]+F[62,x]
F[58,x] = F[37,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[12,x]*F[61,x]
F[61,x] = F[12,x]+F[59,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = F[33,x]+F[48,x]+F[56,x]
F[64,x] = F[65,x]
F[65,x] = F[12,x]*F[66,x]
F[66,x] = F[53,x]+F[67,x]
F[67,x] = F[65,x]
F[68,x] = F[69,x]+F[72,x]
F[69,x] = F[70,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[8,x]
F[72,x] = F[73,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = F[53,x]
F[76,x] = F[73,x]
F[77,x] = F[12,x]*F[78,x]
F[78,x] = F[1,x]+F[101,x]+F[163,x]+F[79,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[81,x]+F[87,x]
F[81,x] = F[39,x]+F[82,x]
F[82,x] = F[37,x]+F[83,x]
F[83,x] = F[33,x]+F[84,x]+F[86,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[12,x]+F[53,x]
F[86,x] = F[12,x]*F[82,x]
F[87,x] = F[46,x]+F[88,x]
F[88,x] = F[47,x]+F[89,x]
F[89,x] = F[100,x]+F[33,x]+F[90,x]+F[98,x]
F[90,x] = F[12,x]*F[91,x]
F[91,x] = F[92,x]+F[95,x]
F[92,x] = F[93,x]
F[93,x] = F[12,x]*F[94,x]
F[94,x] = F[37,x]+F[92,x]
F[95,x] = 2*F[33,x]+F[90,x]+F[96,x]
F[96,x] = F[12,x]*F[97,x]
F[97,x] = F[47,x]+F[95,x]
F[98,x] = F[12,x]*F[99,x]
F[99,x] = F[59,x]+F[67,x]
F[100,x] = F[12,x]*F[88,x]
F[101,x] = F[102,x]*F[12,x]
F[102,x] = F[103,x,1]
F[103,x,k[0]] = F[1,x]+F[104,x,k[0]]+F[151,x,k[0]]+F[153,x,k[0]]+F[161,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]*F[12,x]
F[105,x,k[0]] = F[106,x,k[0]]+F[122,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]+F[115,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]+F[39,x]
F[108,x,k[0]] = F[109,x,k[0]]+F[113,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]*F[112,x,k[0]]
F[111,x,k[0]] = F[1,x]+F[109,x,k[0]]
F[112,x,k[0]] = k[0]*x
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[108,x,k[0]]*F[12,x]
F[115,x,k[0]] = F[116,x,k[0]]+F[82,x]
F[116,x,k[0]] = F[117,x,k[0]]+F[120,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]
F[118,x,k[0]] = F[112,x,k[0]]*F[119,x,k[0]]
F[119,x,k[0]] = F[117,x,k[0]]+F[37,x]
F[120,x,k[0]] = F[121,x,k[0]]
F[121,x,k[0]] = F[116,x,k[0]]*F[12,x]
F[122,x,k[0]] = F[123,x,k[0]]+F[134,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]+F[46,x]
F[124,x,k[0]] = F[125,x,k[0]]+F[130,x,k[0]]
F[125,x,k[0]] = F[126,x,k[0]]+F[128,x,k[0]]+F[33,x]
F[126,x,k[0]] = F[12,x]*F[127,x,k[0]]
F[127,x,k[0]] = F[109,x,k[0]]+F[125,x,k[0]]
F[128,x,k[0]] = F[112,x,k[0]]*F[129,x,k[0]]
F[129,x,k[0]] = F[125,x,k[0]]+F[37,x]
F[130,x,k[0]] = 2*F[33,x]+F[131,x,k[0]]+F[133,x,k[0]]
F[131,x,k[0]] = F[12,x]*F[132,x,k[0]]
F[132,x,k[0]] = F[113,x,k[0]]+F[130,x,k[0]]
F[133,x,k[0]] = F[12,x]*F[124,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]+F[88,x]
F[135,x,k[0]] = F[136,x,k[0]]+F[141,x,k[0]]
F[136,x,k[0]] = 2*F[33,x]+F[137,x,k[0]]+F[139,x,k[0]]
F[137,x,k[0]] = F[12,x]*F[138,x,k[0]]
F[138,x,k[0]] = F[117,x,k[0]]+F[136,x,k[0]]
F[139,x,k[0]] = F[112,x,k[0]]*F[140,x,k[0]]
F[140,x,k[0]] = F[136,x,k[0]]+F[47,x]
F[141,x,k[0]] = 3*F[33,x]+F[142,x,k[0]]+F[150,x,k[0]]
F[142,x,k[0]] = F[12,x]*F[143,x,k[0]]
F[143,x,k[0]] = F[144,x,k[0]]+F[147,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]
F[145,x,k[0]] = F[12,x]*F[146,x,k[0]]
F[146,x,k[0]] = F[117,x,k[0]]+F[144,x,k[0]]
F[147,x,k[0]] = 3*F[33,x]+F[142,x,k[0]]+F[148,x,k[0]]
F[148,x,k[0]] = F[12,x]*F[149,x,k[0]]
F[149,x,k[0]] = F[136,x,k[0]]+F[147,x,k[0]]
F[150,x,k[0]] = F[12,x]*F[135,x,k[0]]
F[151,x,k[0]] = F[12,x]*F[152,x,k[0]]
F[152,x,k[0]] = 1/(-1+k[0])*(F[103,x,k[0]]*k[0]-F[103,x,1])
F[153,x,k[0]] = F[112,x,k[0]]*F[154,x,k[0]]
F[154,x,k[0]] = F[1,x]+F[153,x,k[0]]+F[155,x,k[0]]+F[159,x,k[0]]
F[155,x,k[0]] = F[12,x]*F[156,x,k[0]]
F[156,x,k[0]] = F[157,x,k[0]]+F[158,x,k[0]]
F[157,x,k[0]] = F[111,x,k[0]]+F[119,x,k[0]]
F[158,x,k[0]] = F[129,x,k[0]]+F[140,x,k[0]]
F[159,x,k[0]] = F[12,x]*F[160,x,k[0]]
F[160,x,k[0]] = 1/(-1+k[0])*(F[154,x,k[0]]*k[0]-F[154,x,1])
F[161,x,k[0]] = F[12,x]*F[162,x,k[0]]
F[162,x,k[0]] = 1/(-1+k[0])*(F[154,x,k[0]]*k[0]-F[154,x,1])
F[163,x] = F[153,x,1]
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_{4}\! \left(x \right)+F_{77}\! \left(x \right)
F_{4}\! \left(x \right) = F_{12}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{30}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{16}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{13}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{8}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{17}\! \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_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = x^{2}
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{21}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{68}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{8}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)+F_{56}\! \left(x \right)
F_{33}\! \left(x \right) = 0
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{43}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \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) = F_{44}\! \left(x \right)+F_{50}\! \left(x \right)
F_{44}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{37}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{33}\! \left(x \right)+F_{45}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{37}\! \left(x \right)+F_{47}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{55}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{55}\! \left(x \right) = F_{51}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{62}\! \left(x \right)
F_{58}\! \left(x \right) = F_{37}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right)+F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = F_{33}\! \left(x \right)+F_{48}\! \left(x \right)+F_{56}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{53}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{65}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{72}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{8}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{53}\! \left(x \right)
F_{76}\! \left(x \right) = F_{73}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{1}\! \left(x \right)+F_{101}\! \left(x \right)+F_{163}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{87}\! \left(x \right)
F_{81}\! \left(x \right) = F_{39}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{37}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{33}\! \left(x \right)+F_{84}\! \left(x \right)+F_{86}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{12}\! \left(x \right)+F_{53}\! \left(x \right)
F_{86}\! \left(x \right) = F_{12}\! \left(x \right) F_{82}\! \left(x \right)
F_{87}\! \left(x \right) = F_{46}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{47}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{100}\! \left(x \right)+F_{33}\! \left(x \right)+F_{90}\! \left(x \right)+F_{98}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{95}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{37}\! \left(x \right)+F_{92}\! \left(x \right)
F_{95}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{90}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{47}\! \left(x \right)+F_{95}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{59}\! \left(x \right)+F_{67}\! \left(x \right)
F_{100}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{12}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x , 1\right)
F_{103}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{104}\! \left(x , y\right)+F_{151}\! \left(x , y\right)+F_{153}\! \left(x , y\right)+F_{161}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{122}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{39}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{113}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right) F_{112}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{109}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = y x
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{82}\! \left(x \right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{120}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{119}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{37}\! \left(x \right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{46}\! \left(x \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) = F_{126}\! \left(x , y\right)+F_{128}\! \left(x , y\right)+F_{33}\! \left(x \right)
F_{126}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{127}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{125}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{129}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{37}\! \left(x \right)
F_{130}\! \left(x , y\right) = 2 F_{33}\! \left(x \right)+F_{131}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{132}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{130}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{124}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{88}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = 2 F_{33}\! \left(x \right)+F_{137}\! \left(x , y\right)+F_{139}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{138}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{136}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{140}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{47}\! \left(x \right)
F_{141}\! \left(x , y\right) = 3 F_{33}\! \left(x \right)+F_{142}\! \left(x , y\right)+F_{150}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{143}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{147}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{146}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{144}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = 3 F_{33}\! \left(x \right)+F_{142}\! \left(x , y\right)+F_{148}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{149}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{147}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{135}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = -\frac{-y F_{103}\! \left(x , y\right)+F_{103}\! \left(x , 1\right)}{-1+y}
F_{153}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{154}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{153}\! \left(x , y\right)+F_{155}\! \left(x , y\right)+F_{159}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{156}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{158}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{119}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{140}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{160}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = -\frac{-y F_{154}\! \left(x , y\right)+F_{154}\! \left(x , 1\right)}{-1+y}
F_{161}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = -\frac{-y F_{154}\! \left(x , y\right)+F_{154}\! \left(x , 1\right)}{-1+y}
F_{163}\! \left(x \right) = F_{153}\! \left(x , 1\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_4(x) + F_77(x))
Eq(F_4(x), F_12(x)*F_5(x))
Eq(F_5(x), F_30(x) + F_6(x))
Eq(F_6(x), F_16(x) + F_7(x))
Eq(F_7(x), F_1(x) + F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_12(x))
Eq(F_10(x), F_11(x) + F_13(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_8(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_8(x))
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_12(x)*F_19(x))
Eq(F_19(x), F_1(x) + F_17(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_12(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_26(x))
Eq(F_23(x), F_12(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), x**2)
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_21(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_12(x)*F_27(x))
Eq(F_30(x), F_31(x) + F_68(x))
Eq(F_31(x), F_32(x) + F_8(x))
Eq(F_32(x), F_33(x) + F_34(x) + F_56(x))
Eq(F_33(x), 0)
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_43(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_12(x)*F_39(x))
Eq(F_39(x), F_1(x) + F_37(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), F_44(x) + F_50(x))
Eq(F_44(x), F_33(x) + F_34(x) + F_45(x))
Eq(F_45(x), F_12(x)*F_46(x))
Eq(F_46(x), F_37(x) + F_47(x))
Eq(F_47(x), F_33(x) + F_45(x) + F_48(x))
Eq(F_48(x), F_12(x)*F_49(x))
Eq(F_49(x), F_37(x) + F_47(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_12(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_55(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_12(x)*F_37(x))
Eq(F_55(x), F_51(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_62(x))
Eq(F_58(x), F_37(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_12(x)*F_61(x))
Eq(F_61(x), F_12(x) + F_59(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), F_33(x) + F_48(x) + F_56(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_12(x)*F_66(x))
Eq(F_66(x), F_53(x) + F_67(x))
Eq(F_67(x), F_65(x))
Eq(F_68(x), F_69(x) + F_72(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_8(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), F_53(x))
Eq(F_76(x), F_73(x))
Eq(F_77(x), F_12(x)*F_78(x))
Eq(F_78(x), F_1(x) + F_101(x) + F_163(x) + F_79(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_87(x))
Eq(F_81(x), F_39(x) + F_82(x))
Eq(F_82(x), F_37(x) + F_83(x))
Eq(F_83(x), F_33(x) + F_84(x) + F_86(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_12(x) + F_53(x))
Eq(F_86(x), F_12(x)*F_82(x))
Eq(F_87(x), F_46(x) + F_88(x))
Eq(F_88(x), F_47(x) + F_89(x))
Eq(F_89(x), F_100(x) + F_33(x) + F_90(x) + F_98(x))
Eq(F_90(x), F_12(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_95(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_12(x)*F_94(x))
Eq(F_94(x), F_37(x) + F_92(x))
Eq(F_95(x), 2*F_33(x) + F_90(x) + F_96(x))
Eq(F_96(x), F_12(x)*F_97(x))
Eq(F_97(x), F_47(x) + F_95(x))
Eq(F_98(x), F_12(x)*F_99(x))
Eq(F_99(x), F_59(x) + F_67(x))
Eq(F_100(x), F_12(x)*F_88(x))
Eq(F_101(x), F_102(x)*F_12(x))
Eq(F_102(x), F_103(x, 1))
Eq(F_103(x, k_0), F_1(x) + F_104(x, k_0) + F_151(x, k_0) + F_153(x, k_0) + F_161(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0)*F_12(x))
Eq(F_105(x, k_0), F_106(x, k_0) + F_122(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0) + F_115(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0) + F_39(x))
Eq(F_108(x, k_0), F_109(x, k_0) + F_113(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0)*F_112(x, k_0))
Eq(F_111(x, k_0), F_1(x) + F_109(x, k_0))
Eq(F_112(x, k_0), k_0*x)
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_108(x, k_0)*F_12(x))
Eq(F_115(x, k_0), F_116(x, k_0) + F_82(x))
Eq(F_116(x, k_0), F_117(x, k_0) + F_120(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0))
Eq(F_118(x, k_0), F_112(x, k_0)*F_119(x, k_0))
Eq(F_119(x, k_0), F_117(x, k_0) + F_37(x))
Eq(F_120(x, k_0), F_121(x, k_0))
Eq(F_121(x, k_0), F_116(x, k_0)*F_12(x))
Eq(F_122(x, k_0), F_123(x, k_0) + F_134(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0) + F_46(x))
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) + F_33(x))
Eq(F_126(x, k_0), F_12(x)*F_127(x, k_0))
Eq(F_127(x, k_0), F_109(x, k_0) + F_125(x, k_0))
Eq(F_128(x, k_0), F_112(x, k_0)*F_129(x, k_0))
Eq(F_129(x, k_0), F_125(x, k_0) + F_37(x))
Eq(F_130(x, k_0), F_131(x, k_0) + F_133(x, k_0) + 2*F_33(x))
Eq(F_131(x, k_0), F_12(x)*F_132(x, k_0))
Eq(F_132(x, k_0), F_113(x, k_0) + F_130(x, k_0))
Eq(F_133(x, k_0), F_12(x)*F_124(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0) + F_88(x))
Eq(F_135(x, k_0), F_136(x, k_0) + F_141(x, k_0))
Eq(F_136(x, k_0), F_137(x, k_0) + F_139(x, k_0) + 2*F_33(x))
Eq(F_137(x, k_0), F_12(x)*F_138(x, k_0))
Eq(F_138(x, k_0), F_117(x, k_0) + F_136(x, k_0))
Eq(F_139(x, k_0), F_112(x, k_0)*F_140(x, k_0))
Eq(F_140(x, k_0), F_136(x, k_0) + F_47(x))
Eq(F_141(x, k_0), F_142(x, k_0) + F_150(x, k_0) + 3*F_33(x))
Eq(F_142(x, k_0), F_12(x)*F_143(x, k_0))
Eq(F_143(x, k_0), F_144(x, k_0) + F_147(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0))
Eq(F_145(x, k_0), F_12(x)*F_146(x, k_0))
Eq(F_146(x, k_0), F_117(x, k_0) + F_144(x, k_0))
Eq(F_147(x, k_0), F_142(x, k_0) + F_148(x, k_0) + 3*F_33(x))
Eq(F_148(x, k_0), F_12(x)*F_149(x, k_0))
Eq(F_149(x, k_0), F_136(x, k_0) + F_147(x, k_0))
Eq(F_150(x, k_0), F_12(x)*F_135(x, k_0))
Eq(F_151(x, k_0), F_12(x)*F_152(x, k_0))
Eq(F_152(x, k_0), (k_0*F_103(x, k_0) - F_103(x, 1))/(k_0 - 1))
Eq(F_153(x, k_0), F_112(x, k_0)*F_154(x, k_0))
Eq(F_154(x, k_0), F_1(x) + F_153(x, k_0) + F_155(x, k_0) + F_159(x, k_0))
Eq(F_155(x, k_0), F_12(x)*F_156(x, k_0))
Eq(F_156(x, k_0), F_157(x, k_0) + F_158(x, k_0))
Eq(F_157(x, k_0), F_111(x, k_0) + F_119(x, k_0))
Eq(F_158(x, k_0), F_129(x, k_0) + F_140(x, k_0))
Eq(F_159(x, k_0), F_12(x)*F_160(x, k_0))
Eq(F_160(x, k_0), (k_0*F_154(x, k_0) - F_154(x, 1))/(k_0 - 1))
Eq(F_161(x, k_0), F_12(x)*F_162(x, k_0))
Eq(F_162(x, k_0), (-k_0*F_154(x, k_0) + F_154(x, 1))/(1 - k_0))
Eq(F_163(x), F_153(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [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": 1, "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], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [1, 1], [1, 1], [3, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}], "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], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"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], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 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": [[0, 0], [0, 0], [0, 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, 0, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 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