0132_0213_0231_1023_1230_3012
Counting sequence:
1, 1, 2, 6, 18, 50, 146, 452, 1466, 4917, 16879, 58911, 208201, 743188, 2674883, 9695533, 35358748, 129646492, 477641404, 1767267507, 6564127338, 24466278137, 91482581541, 343059642517, 1289904193923, 4861946476730, 18367353193821, 69533551112722, 263747952068496, 1002242217165948, 3814986502924722, 14544636040573584, 55534064879226942, 212336130415768153, 812944042155434147, 3116285494916529255, 11959798385875384405, 45950804324645900776, 176733862787045790199, 680425371730039047042, 2622127042276594443678, 10113918591638063714902, 39044429911904711874316, 150853479205085785155957, 583300119592997394497634, 2257117854077249208157793, 8740328711533175226359169, 33868773757191049857645553, 131327898242169370285519911, 509552245179617145833351702, 1978261657756160666210044609, 7684785670514316405595828406, 29869166945772625983093698836, 116157871455782434303870138328, 451959718027953471533877082022, 1759414616608818871132063739795, 6852456927844873497775509899460, 26700952856774851904610656210311, 104088460289122304034089605543499, 405944995127576985731600165394749, 1583850964596120042688320787796469, 6182127958584855650489585578000008, 24139737743045626825715511285812963, 94295850558771979787941942416701797, 368479169875816659479019652923406564, 1440418573150919668872507061924044868, 5632681584560312734993943483739182404, 22033725021956517463358597559627164883, 86218923998960285726185713387161358786, 337485502510215975556783911124089087905, 1321422108420282270489942367582720256013, 5175569924646105559418940502056586888825, 20276890389709399862928999066708652907379, 79463489365077377841208238438864801936378, 311496878311103321137536292823778678958453, 1221395654430378811828760724119447208771698, 4790408930363303911328386211811319083933928, 18793142726809884575211361284615484894137572, 73745243611532458459690151863591723563129914, 289450081175264899454283846043963101289071377, 1136359577947336271931632877028084185016084628, 4462290049988320482463241297544022245872801727, 17526585015616776834735140517976961427117849031, 68854441132780194707888052034767841996079964837, 270557451039395118028642463289329067064487650849, 1063353702922273835973036658043736154220014530508, 4180080073556524734514695828171327654569478807479, 16435314834665426797069144960763566035005229010768, 64633260585762914370496637486147281550459901366586, 254224158304000796523953440778843427065963376744530, 1000134600800354781929399250536544744429655460770748, 3935312233584004685417853572763354169820642055558025, 15487357822491889407128326963778350772127735874186034, 60960876535340415751462563580829661092130144029318833, 239993345518077005168915776623476742746555047356456953, 944973797977428207852605870454939628777665393225008233, 3721443204405954385563870541379246711390215552237021743, 14657929356129575437016877846657032845334098440748182542, 57743358069601357782187700608042856469322583969463361609, 227508830794229349661819540395688854174964678436096221022, 896519947090131496687170070074100632775062369718007829148
Generating function in Maple syntax:
1/2*(-(x^2+x-1)*(x-1)^3*(1-4*x)^(1/2)-2*x^9+2*x^8+2*x^7-6*x^6+x^5-x^3+5*x^2-4*x+1)/x/(x^2+x-1)/(x-1)^3
Generating function in latex syntax:
\frac{-\left(x^{2}+x -1\right) \left(x -1\right)^{3} \sqrt{1-4 x}-2 x^{9}+2 x^{8}+2 x^{7}-6 x^{6}+x^{5}-x^{3}+5 x^{2}-4 x +1}{2 x \left(x^{2}+x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(-x**9 + x**8 + x**7 - 3*x**6 + x**5/2 - x**3/2 + 5*x**2/2 - 2*x + sqrt(1 - 4*x)*(x - 1)**3*(-x**2 - x + 1)/2 + 1/2)/(x*(x - 1)**3*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
x*(x^2+x-1)^2*(x-1)^6*F(x)^2+(x^2+x-1)*(2*x^9-2*x^8-2*x^7+6*x^6-x^5+x^3-5*x^2+4*x-1)*(x-1)^3*F(x)+x^17-2*x^16-x^15+8*x^14-6*x^13-5*x^12+11*x^11-8*x^10+4*x^9+6*x^8-5*x^7-15*x^6+10*x^5+25*x^4-41*x^3+26*x^2-8*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(x^{2}+x -1\right)^{2} \left(x -1\right)^{6} F \! \left(x \right)^{2}+\left(x^{2}+x -1\right) \left(2 x^{9}-2 x^{8}-2 x^{7}+6 x^{6}-x^{5}+x^{3}-5 x^{2}+4 x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+x^{17}-2 x^{16}-x^{15}+8 x^{14}-6 x^{13}-5 x^{12}+11 x^{11}-8 x^{10}+4 x^{9}+6 x^{8}-5 x^{7}-15 x^{6}+10 x^{5}+25 x^{4}-41 x^{3}+26 x^{2}-8 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 18
a(5) = 50
a(6) = 146
a(7) = 452
a(8) = 1466
a(9) = 4917
a(10) = 16879
a(11) = 58911
a(12) = 208201
a(n+5) = 2*(2*n+1)/(n+6)*a(n)+(10+7*n)/(n+6)*a(n+1)-2*(3*n+8)/(n+6)*a(n+2)-(7*n+24)/(n+6)*a(n+3)+2*(3*n+14)/(n+6)*a(n+4)-1/2*(3*n^3-35*n^2+50*n+52)/(n+6), n >= 13
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) = 18
a \! \left(5\right) = 50
a \! \left(6\right) = 146
a \! \left(7\right) = 452
a \! \left(8\right) = 1466
a \! \left(9\right) = 4917
a \! \left(10\right) = 16879
a \! \left(11\right) = 58911
a \! \left(12\right) = 208201
a \! \left(n +5\right) = \frac{2 \left(2 n +1\right) a \! \left(n \right)}{n +6}+\frac{\left(10+7 n \right) a \! \left(n +1\right)}{n +6}-\frac{2 \left(3 n +8\right) a \! \left(n +2\right)}{n +6}-\frac{\left(7 n +24\right) a \! \left(n +3\right)}{n +6}+\frac{2 \left(3 n +14\right) a \! \left(n +4\right)}{n +6}-\frac{3 n^{3}-35 n^{2}+50 n +52}{2 \left(n +6\right)}, \quad n \geq 13
Specification 1
Strategy pack name: requirement_placements_tracked_fusion
Tree: http://www.permpal.com/tree/22170/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[6,x]
F[1,x] = F[2,x]+F[3,x]
F[2,x] = 1
F[3,x] = F[4,x]
F[4,x] = F[1,x]*F[5,x]
F[5,x] = x
F[6,x] = F[7,x]
F[7,x] = F[5,x]*F[8,x]
F[8,x] = F[54,x]+F[9,x]
F[9,x] = F[10,x]+F[27,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[5,x]
F[12,x] = F[13,x]+F[16,x]
F[13,x] = F[14,x]+F[2,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[5,x]
F[16,x] = F[17,x]+F[24,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[5,x]
F[19,x] = F[20,x]+F[21,x]
F[20,x] = F[2,x]+F[5,x]
F[21,x] = F[17,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[17,x]*F[5,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[5,x]
F[26,x] = F[17,x]
F[27,x] = F[28,x]+F[29,x]+F[48,x]
F[28,x] = 0
F[29,x] = F[30,x]*F[5,x]
F[30,x] = F[31,x]+F[36,x]
F[31,x] = F[3,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[5,x]
F[34,x] = F[35,x]+F[5,x]
F[35,x] = F[33,x]
F[36,x] = F[37,x]+F[53,x]
F[37,x] = F[28,x]+F[38,x]+F[48,x]
F[38,x] = F[39,x]*F[5,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[3,x]+F[35,x]
F[41,x] = F[37,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[44,x]*F[5,x]
F[44,x] = F[45,x]+F[47,x]
F[45,x] = F[46,x]
F[46,x] = F[3,x]*F[5,x]
F[47,x] = F[43,x]
F[48,x] = F[49,x]*F[5,x]
F[49,x] = F[3,x]+F[50,x]
F[50,x] = F[28,x]+F[48,x]+F[51,x]
F[51,x] = F[5,x]*F[52,x]
F[52,x] = F[3,x]+F[50,x]
F[53,x] = F[43,x]
F[54,x] = F[55,x]
F[55,x] = F[56,x,1]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[58,x,k[0]] = F[5,x]*F[59,x,k[0]]*F[68,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]+F[78,x,k[0]]
F[60,x,k[0]] = F[49,x]+F[61,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]+F[69,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[5,x]*F[64,x,k[0]]
F[64,x,k[0]] = F[62,x,k[0]]+F[65,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]*F[68,x,k[0]]
F[67,x,k[0]] = k[0]*x
F[68,x,k[0]] = F[2,x]+F[65,x,k[0]]
F[69,x,k[0]] = 2*F[28,x]+F[70,x,k[0]]+F[77,x,k[0]]
F[70,x,k[0]] = F[5,x]*F[71,x,k[0]]
F[71,x,k[0]] = F[69,x,k[0]]+F[72,x,k[0]]
F[72,x,k[0]] = F[28,x]+F[73,x,k[0]]+F[75,x,k[0]]
F[73,x,k[0]] = F[67,x,k[0]]*F[74,x,k[0]]
F[74,x,k[0]] = F[3,x]+F[72,x,k[0]]
F[75,x,k[0]] = F[5,x]*F[76,x,k[0]]
F[76,x,k[0]] = F[65,x,k[0]]+F[72,x,k[0]]
F[77,x,k[0]] = F[5,x]*F[61,x,k[0]]
F[78,x,k[0]] = (F[57,x,k[0]]*k[0]-F[57,x,1])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{1}\! \left(x \right) = F_{2}\! \left(x \right)+F_{3}\! \left(x \right)
F_{2}\! \left(x \right) = 1
F_{3}\! \left(x \right) = F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = x
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{54}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{27}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{5}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{16}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{2}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{5}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{24}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{5}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{21}\! \left(x \right) = F_{17}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{17}\! \left(x \right) F_{5}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{5}\! \left(x \right)
F_{26}\! \left(x \right) = F_{17}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)+F_{48}\! \left(x \right)
F_{28}\! \left(x \right) = 0
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{5}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{36}\! \left(x \right)
F_{31}\! \left(x \right) = F_{3}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{5}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{5}\! \left(x \right)
F_{35}\! \left(x \right) = F_{33}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{53}\! \left(x \right)
F_{37}\! \left(x \right) = F_{28}\! \left(x \right)+F_{38}\! \left(x \right)+F_{48}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{5}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{3}\! \left(x \right)+F_{35}\! \left(x \right)
F_{41}\! \left(x \right) = F_{37}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right) F_{5}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{3}\! \left(x \right) F_{5}\! \left(x \right)
F_{47}\! \left(x \right) = F_{43}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right) F_{5}\! \left(x \right)
F_{49}\! \left(x \right) = F_{3}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{28}\! \left(x \right)+F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{5}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{3}\! \left(x \right)+F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = F_{43}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x , 1\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{59}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{49}\! \left(x \right)+F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = y x
F_{68}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{65}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = 2 F_{28}\! \left(x \right)+F_{70}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{73}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{67}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{3}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{65}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{61}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = \frac{y F_{57}\! \left(x , y\right)-F_{57}\! \left(x , 1\right)}{-1+y}
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_6(x))
Eq(F_1(x), F_2(x) + F_3(x))
Eq(F_2(x), 1)
Eq(F_3(x), F_4(x))
Eq(F_4(x), F_1(x)*F_5(x))
Eq(F_5(x), x)
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_5(x)*F_8(x))
Eq(F_8(x), F_54(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_27(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_5(x))
Eq(F_12(x), F_13(x) + F_16(x))
Eq(F_13(x), F_14(x) + F_2(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_5(x))
Eq(F_16(x), F_17(x) + F_24(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_5(x))
Eq(F_19(x), F_20(x) + F_21(x))
Eq(F_20(x), F_2(x) + F_5(x))
Eq(F_21(x), F_17(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_17(x)*F_5(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_5(x))
Eq(F_26(x), F_17(x))
Eq(F_27(x), F_28(x) + F_29(x) + F_48(x))
Eq(F_28(x), 0)
Eq(F_29(x), F_30(x)*F_5(x))
Eq(F_30(x), F_31(x) + F_36(x))
Eq(F_31(x), F_3(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_5(x))
Eq(F_34(x), F_35(x) + F_5(x))
Eq(F_35(x), F_33(x))
Eq(F_36(x), F_37(x) + F_53(x))
Eq(F_37(x), F_28(x) + F_38(x) + F_48(x))
Eq(F_38(x), F_39(x)*F_5(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_3(x) + F_35(x))
Eq(F_41(x), F_37(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x)*F_5(x))
Eq(F_44(x), F_45(x) + F_47(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_3(x)*F_5(x))
Eq(F_47(x), F_43(x))
Eq(F_48(x), F_49(x)*F_5(x))
Eq(F_49(x), F_3(x) + F_50(x))
Eq(F_50(x), F_28(x) + F_48(x) + F_51(x))
Eq(F_51(x), F_5(x)*F_52(x))
Eq(F_52(x), F_3(x) + F_50(x))
Eq(F_53(x), F_43(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_56(x, 1))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_58(x, k_0), F_5(x)*F_59(x, k_0)*F_68(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0) + F_78(x, k_0))
Eq(F_60(x, k_0), F_49(x) + F_61(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0) + F_69(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_5(x)*F_64(x, k_0))
Eq(F_64(x, k_0), F_62(x, k_0) + F_65(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0)*F_68(x, k_0))
Eq(F_67(x, k_0), k_0*x)
Eq(F_68(x, k_0), F_2(x) + F_65(x, k_0))
Eq(F_69(x, k_0), 2*F_28(x) + F_70(x, k_0) + F_77(x, k_0))
Eq(F_70(x, k_0), F_5(x)*F_71(x, k_0))
Eq(F_71(x, k_0), F_69(x, k_0) + F_72(x, k_0))
Eq(F_72(x, k_0), F_28(x) + F_73(x, k_0) + F_75(x, k_0))
Eq(F_73(x, k_0), F_67(x, k_0)*F_74(x, k_0))
Eq(F_74(x, k_0), F_3(x) + F_72(x, k_0))
Eq(F_75(x, k_0), F_5(x)*F_76(x, k_0))
Eq(F_76(x, k_0), F_65(x, k_0) + F_72(x, k_0))
Eq(F_77(x, k_0), F_5(x)*F_61(x, k_0))
Eq(F_78(x, k_0), (-k_0*F_57(x, k_0) + F_57(x, 1))/(1 - k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "limited_insertion": true, "maxreqlen": 2, "strategy_class": "RequirementInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "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.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "requirement_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": [0, 2, 3, 1], "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, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"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": [0, 2, 3, 1], "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": [[{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 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": [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_insertion", "gps": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [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": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}]]}, {"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": [[1, 2]]}, {"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], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [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": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}], [{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[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, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [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": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [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": [[{"patt": [0, 1], "pos": [[0, 1], [0, 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, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [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": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}, {"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": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}]]}, {"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]]}]]}, {"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]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 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