0132_0231_1230_2013_3012
Counting sequence:
1, 1, 2, 6, 19, 56, 162, 484, 1521, 5002, 17000, 59071, 208397, 743406, 2675090, 9695664, 35358685, 129646030, 477640196, 1767264975, 6564122529, 24466269490, 91482566510, 343059616961, 1289904151119, 4861946405776, 18367353077052, 69533550921529, 263747951756561, 1002242216658298, 3814986502100018, 14544636039235464, 55534064877057653, 212336130412253526, 812944042149742204, 3116285494907313791, 11959798385860467177, 45950804324621757274, 176733862787006717606, 680425371729975817965, 2622127042276492127839, 10113918591637898154560, 39044429911904443981380, 150853479205085351684521, 583300119592996693113625, 2257117854077248073281154, 8740328711533173390075690, 33868773757191046886460885, 131327898242169365478025411, 509552245179617138054644292, 1978261657756160653623812480, 7684785670514316385230856581, 29869166945772625950142460437, 116157871455782434250553891406, 451959718027953471447609557654, 1759414616608818870992479927011, 6852456927844873497549658518267, 26700952856774851904245220969644, 104088460289122304033498318872196, 405944995127576985730643443430477, 1583850964596120042686772779105625, 6182127958584855650487080847286546, 24139737743045626825711458546347122, 94295850558771979787935384946457656, 368479169875816659479009042713628325, 1440418573150919668872489894243950694, 5632681584560312734993915705849234540, 22033725021956517463358552614057043615, 86218923998960285726185640663701206521, 337485502510215975556783793455058727210, 1321422108420282270489942177190229651734, 5175569924646105559418940193995065828245, 20276890389709399862928998568254641142495, 79463489365077377841208237632349269006336, 311496878311103321137536291518809134154260, 1221395654430378811828760722007962130923369, 4790408930363303911328386208394864461162345, 18793142726809884575211361279087545193393490, 73745243611532458459690151854647329239484826, 289450081175264899454283846029490767264547385, 1136359577947336271931632877004667456667775179, 4462290049988320482463241297506133183499822220, 17526585015616776834735140517915655636396408160, 68854441132780194707888052034668647142985386541, 270557451039395118028642463289168566420671467605, 1063353702922273835973036658043476458723103598574, 4180080073556524734514695828170907458428751515430, 16435314834665426797069144960762886143367590603275, 64633260585762914370496637486146181462681535476731, 254224158304000796523953440778841647086547372249900, 1000134600800354781929399250536541864362461090181844, 3935312233584004685417853572763349509774031680262765, 15487357822491889407128326963778343232013931128082665, 60960876535340415751462563580829648891969728907693346, 239993345518077005168915776623476723006280827488493410, 944973797977428207852605870454939596837230758235176509, 3721443204405954385563870541379246659709506697378975595, 14657929356129575437016877846657032761712954950900045420, 57743358069601357782187700608042856334020731624756910536, 227508830794229349661819540395688853956041682601541356285, 896519947090131496687170070074100632420837521538746227869
Generating function in Maple syntax:
1/2*(-(x-1)^4*(-4*x+1)^(1/2)+2*x^5+3*x^4-4*x^3+6*x^2-4*x+1)/x/(x-1)^4
Generating function in latex syntax:
\frac{-\left(x -1\right)^{4} \sqrt{-4 x +1}+2 x^{5}+3 x^{4}-4 x^{3}+6 x^{2}-4 x +1}{2 x \left(x -1\right)^{4}}
Generating function in sympy syntax:
(x**5 + 3*x**4/2 - 2*x**3 + 3*x**2 - 2*x - sqrt(1 - 4*x)*(x - 1)**4/2 + 1/2)/(x*(x - 1)**4)
Implicit equation for the generating function in Maple syntax:
x*(x-1)^8*F(x)^2-(2*x^5+3*x^4-4*x^3+6*x^2-4*x+1)*(x-1)^4*F(x)+x^9+4*x^8-10*x^7+30*x^6-54*x^5+67*x^4-55*x^3+28*x^2-8*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(x -1\right)^{8} F \! \left(x \right)^{2}-\left(2 x^{5}+3 x^{4}-4 x^{3}+6 x^{2}-4 x +1\right) \left(x -1\right)^{4} F \! \left(x \right)+x^{9}+4 x^{8}-10 x^{7}+30 x^{6}-54 x^{5}+67 x^{4}-55 x^{3}+28 x^{2}-8 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 56
a(6) = 162
a(1+n) = 2*(2*n+1)/(n+2)*a(n)-1/2*(n-1)*(2*n^3-9*n^2+4*n+4)/(n+2), n >= 7
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) = 56
a \! \left(6\right) = 162
a \! \left(1+n \right) = \frac{2 \left(2 n +1\right) a \! \left(n \right)}{n +2}-\frac{\left(n -1\right) \left(2 n^{3}-9 n^{2}+4 n +4\right)}{2 \left(n +2\right)}, \quad n \geq 7
Specification 1
Strategy pack name: requirement_placements_tracked_fusion
Tree: http://permpal.com/tree/21719/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[7,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] = F[6,x,1]
F[6,x,k[0]] = k[0]*x
F[7,x] = F[8,x]
F[8,x] = F[5,x]*F[9,x]
F[9,x] = F[10,x]+F[66,x]
F[10,x] = F[11,x]+F[33,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[5,x]
F[13,x] = F[14,x]+F[17,x]
F[14,x] = F[15,x]+F[2,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]*F[5,x]
F[17,x] = F[18,x]+F[28,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[5,x]
F[20,x] = F[21,x]+F[22,x]
F[21,x] = F[2,x]+F[5,x]
F[22,x] = F[18,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[5,x]
F[25,x] = F[26,x]+F[27,x]
F[26,x] = F[5,x]
F[27,x] = F[23,x]
F[28,x] = F[29,x]
F[29,x] = F[30,x]*F[5,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[15,x]
F[32,x] = F[28,x]
F[33,x] = F[34,x]+F[35,x]+F[36,x]
F[34,x] = 0
F[35,x] = F[10,x]*F[5,x]
F[36,x] = F[37,x]*F[5,x]
F[37,x] = F[38,x]+F[42,x]
F[38,x] = F[3,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[41,x]*F[5,x]
F[41,x] = F[15,x]+F[39,x]
F[42,x] = F[43,x]+F[61,x]
F[43,x] = F[34,x]+F[44,x]+F[49,x]
F[44,x] = F[45,x]*F[5,x]
F[45,x] = F[3,x]+F[46,x]
F[46,x] = F[34,x]+F[44,x]+F[47,x]
F[47,x] = F[48,x]*F[5,x]
F[48,x] = F[3,x]+F[46,x]
F[49,x] = F[5,x]*F[50,x]
F[50,x] = F[51,x]+F[55,x]
F[51,x] = F[3,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[5,x]*F[54,x]
F[54,x] = F[5,x]+F[52,x]
F[55,x] = F[43,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[5,x]*F[58,x]
F[58,x] = F[59,x]+F[60,x]
F[59,x] = F[52,x]
F[60,x] = F[56,x]
F[61,x] = F[62,x]
F[62,x] = F[5,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[39,x]
F[65,x] = F[61,x]
F[66,x] = F[67,x]
F[67,x] = F[68,x,1]
F[68,x,k[0]] = F[69,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[5,x]*F[71,x,k[0]]*F[74,x,k[0]]
F[71,x,k[0]] = F[2,x]+F[72,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]
F[73,x,k[0]] = F[6,x,k[0]]*F[71,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]+F[84,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]+F[79,x,k[0]]
F[76,x,k[0]] = F[3,x]+F[77,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[6,x,k[0]]*F[76,x,k[0]]
F[79,x,k[0]] = F[46,x]+F[80,x,k[0]]
F[80,x,k[0]] = 2*F[34,x]+F[81,x,k[0]]+F[83,x,k[0]]
F[81,x,k[0]] = F[5,x]*F[82,x,k[0]]
F[82,x,k[0]] = F[77,x,k[0]]+F[80,x,k[0]]
F[83,x,k[0]] = F[6,x,k[0]]*F[79,x,k[0]]
F[84,x,k[0]] = 1/(-1+k[0])*(F[69,x,k[0]]*k[0]-F[69,x,1])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \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) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = y x
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{5}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{66}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{33}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{5}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{17}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right) F_{5}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{28}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{5}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)
F_{21}\! \left(x \right) = F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{5}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)
F_{26}\! \left(x \right) = F_{5}\! \left(x \right)
F_{27}\! \left(x \right) = F_{23}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
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_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{15}\! \left(x \right)
F_{32}\! \left(x \right) = F_{28}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{34}\! \left(x \right) = 0
F_{35}\! \left(x \right) = F_{10}\! \left(x \right) F_{5}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{5}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{42}\! \left(x \right)
F_{38}\! \left(x \right) = F_{3}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right) F_{5}\! \left(x \right)
F_{41}\! \left(x \right) = F_{15}\! \left(x \right)+F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{61}\! \left(x \right)
F_{43}\! \left(x \right) = F_{34}\! \left(x \right)+F_{44}\! \left(x \right)+F_{49}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right) F_{5}\! \left(x \right)
F_{45}\! \left(x \right) = F_{3}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{34}\! \left(x \right)+F_{44}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right) F_{5}\! \left(x \right)
F_{48}\! \left(x \right) = F_{3}\! \left(x \right)+F_{46}\! \left(x \right)
F_{49}\! \left(x \right) = F_{5}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{55}\! \left(x \right)
F_{51}\! \left(x \right) = F_{3}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{5}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{5}\! \left(x \right)+F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{43}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{5}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{52}\! \left(x \right)
F_{60}\! \left(x \right) = F_{56}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{5}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{39}\! \left(x \right)
F_{65}\! \left(x \right) = F_{61}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x , 1\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{71}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{71}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{3}\! \left(x \right)+F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{76}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{46}\! \left(x \right)+F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = 2 F_{34}\! \left(x \right)+F_{81}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{77}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{79}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = \frac{F_{69}\! \left(x , y\right) y -F_{69}\! \left(x , 1\right)}{-1+y}
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_7(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), F_6(x, 1))
Eq(F_6(x, k_0), k_0*x)
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_5(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_66(x))
Eq(F_10(x), F_11(x) + F_33(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_5(x))
Eq(F_13(x), F_14(x) + F_17(x))
Eq(F_14(x), F_15(x) + F_2(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)*F_5(x))
Eq(F_17(x), F_18(x) + F_28(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_5(x))
Eq(F_20(x), F_21(x) + F_22(x))
Eq(F_21(x), F_2(x) + F_5(x))
Eq(F_22(x), F_18(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_5(x))
Eq(F_25(x), F_26(x) + F_27(x))
Eq(F_26(x), F_5(x))
Eq(F_27(x), F_23(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)*F_5(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_15(x))
Eq(F_32(x), F_28(x))
Eq(F_33(x), F_34(x) + F_35(x) + F_36(x))
Eq(F_34(x), 0)
Eq(F_35(x), F_10(x)*F_5(x))
Eq(F_36(x), F_37(x)*F_5(x))
Eq(F_37(x), F_38(x) + F_42(x))
Eq(F_38(x), F_3(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_41(x)*F_5(x))
Eq(F_41(x), F_15(x) + F_39(x))
Eq(F_42(x), F_43(x) + F_61(x))
Eq(F_43(x), F_34(x) + F_44(x) + F_49(x))
Eq(F_44(x), F_45(x)*F_5(x))
Eq(F_45(x), F_3(x) + F_46(x))
Eq(F_46(x), F_34(x) + F_44(x) + F_47(x))
Eq(F_47(x), F_48(x)*F_5(x))
Eq(F_48(x), F_3(x) + F_46(x))
Eq(F_49(x), F_5(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_55(x))
Eq(F_51(x), F_3(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_5(x)*F_54(x))
Eq(F_54(x), F_5(x) + F_52(x))
Eq(F_55(x), F_43(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_5(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_60(x))
Eq(F_59(x), F_52(x))
Eq(F_60(x), F_56(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_5(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_39(x))
Eq(F_65(x), F_61(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_68(x, 1))
Eq(F_68(x, k_0), F_69(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_5(x)*F_71(x, k_0)*F_74(x, k_0))
Eq(F_71(x, k_0), F_2(x) + F_72(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0))
Eq(F_73(x, k_0), F_6(x, k_0)*F_71(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0) + F_84(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0) + F_79(x, k_0))
Eq(F_76(x, k_0), F_3(x) + F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_6(x, k_0)*F_76(x, k_0))
Eq(F_79(x, k_0), F_46(x) + F_80(x, k_0))
Eq(F_80(x, k_0), 2*F_34(x) + F_81(x, k_0) + F_83(x, k_0))
Eq(F_81(x, k_0), F_5(x)*F_82(x, k_0))
Eq(F_82(x, k_0), F_77(x, k_0) + F_80(x, k_0))
Eq(F_83(x, k_0), F_6(x, k_0)*F_79(x, k_0))
Eq(F_84(x, k_0), (k_0*F_69(x, k_0) - F_69(x, 1))/(k_0 - 1))
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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "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], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[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, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}, {"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], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "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, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": 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"pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"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, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 3]]}]}], "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]]}], "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]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[2, 3]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 4], [0, 4]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 3]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 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