0132_1023_1230_1302_3102
Counting sequence:
1, 1, 2, 6, 19, 51, 123, 280, 613, 1308, 2742, 5678, 11656, 23779, 48290, 97735, 197303, 397529, 799737, 1606986, 3226059, 6471598, 12974628, 26000016, 52082054, 104296701, 208807808, 417962385, 836485693, 1673878803, 3349225647, 6700826428, 13405495681, 26817208944, 53644477890, 107305232930, 214636802548, 429316218439, 858701386382, 1717514335051, 3435209181299, 6870710435453, 13741893454293, 27484551564126, 54970340366439, 109942682625826, 219888604381968, 439782449786340, 879573379724498, 1759160480622273, 3518343162568652, 7036722247633653, 14073502619086681, 28147099284487959, 56294350739108715, 112588947694663600, 225178293775904893, 450357232154832324, 900715507299263502, 1801432702191146966, 3602868134964511264, 7205740688103858283, 14411488524964768058, 28822988616861421711, 57645995949411778799, 115292022181444376801, 230584093361198506353, 461168266003327582770, 922336660285895486403, 1844673528131961861718, 3689347392103334931132, 7378695327606251956728, 14757391534451497213406, 29514784491541569818949, 59029571284960708327640, 118059146294437560734745, 236118298615268834236213, 472236606981447525316059, 944473229740198620239847, 1888946485008610666928356, 3777893011322738329910329, 7555786089479207082320088, 15111572287097661583190298, 30223144749168301007427146, 60446289781448827274447884, 120892580020982857649532751, 241785160783163143659292838, 483570322765608918779446675, 967140647471697897379978283, 1934281298083158486041899013, 3868562601246559723186821837, 7737125210713124888758606278, 15474250434726497971005195231, 30948500890973249577883331914, 61897001816767000985127584040, 123794003689874757435489025740, 247588007470910772165572825258, 495176015089323557090974277769, 990352030417310384236371952292, 1980704061220786051286995924221, 3961408123066400655442667260369
Generating function in Maple syntax:
(3*x^8-4*x^7-x^6+2*x^5+2*x^4+4*x^3-9*x^2+5*x-1)/(2*x-1)/(x^2+x-1)/(x-1)^3
Generating function in latex syntax:
\frac{3 x^{8}-4 x^{7}-x^{6}+2 x^{5}+2 x^{4}+4 x^{3}-9 x^{2}+5 x -1}{\left(2 x -1\right) \left(x^{2}+x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(3*x**8 - 4*x**7 - x**6 + 2*x**5 + 2*x**4 + 4*x**3 - 9*x**2 + 5*x - 1)/((x - 1)**3*(2*x - 1)*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
-(2*x-1)*(x^2+x-1)*(x-1)^3*F(x)+3*x^8-4*x^7-x^6+2*x^5+2*x^4+4*x^3-9*x^2+5*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right) \left(x^{2}+x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+3 x^{8}-4 x^{7}-x^{6}+2 x^{5}+2 x^{4}+4 x^{3}-9 x^{2}+5 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,1/40*(24*5^(1/2)-80)*(-1/2*5^(1/2)-1/2)^(-n)+1/40*(-24*5^(1/2)-80)*(1/2*5^(1/2)-1/2)^(-n)-1/2*n^2+1/2*n+25/8*2^n-2)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ \frac{\left(24 \sqrt{5}-80\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{40}+\frac{\left(-24 \sqrt{5}-80\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{40}-\frac{n^{2}}{2}+\frac{n}{2}+\\\frac{25 \,2^{n}}{8}-2 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 51
a(6) = 123
a(7) = 280
a(8) = 613
a(n+3) = -2*a(n)-a(n+1)+3*a(n+2)-1/2*(-1+n)*(n-4), n >= 9
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) = 51
a \! \left(6\right) = 123
a \! \left(7\right) = 280
a \! \left(8\right) = 613
a \! \left(n +3\right) = -2 a \! \left(n \right)-a \! \left(n +1\right)+3 a \! \left(n +2\right)-\frac{\left(-1+n \right) \left(n -4\right)}{2}, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/19602/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[42,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[21,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[10,x]+F[17,x]
F[17,x] = F[14,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[14,x]
F[21,x] = F[22,x]+F[23,x]+F[39,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[28,x]
F[25,x] = F[26,x]+F[4,x]
F[26,x] = F[27,x]
F[27,x] = F[25,x]*F[4,x]
F[28,x] = F[29,x]+F[31,x]
F[29,x] = F[22,x]+F[23,x]+F[30,x]
F[30,x] = F[14,x]*F[4,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[25,x]+F[37,x]
F[37,x] = F[34,x]+F[38,x]
F[38,x] = F[32,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[14,x]+F[41,x]
F[41,x] = F[35,x]
F[42,x] = F[43,x]+F[53,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[47,x]
F[46,x] = F[1,x]+F[14,x]
F[47,x] = F[43,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[43,x]
F[52,x] = F[48,x]
F[53,x] = F[22,x]+F[54,x]+F[86,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[56,x]+F[64,x]
F[56,x] = F[57,x]+F[60,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[1,x]+F[57,x]
F[60,x] = F[22,x]+F[23,x]+F[61,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[14,x]+F[63,x]
F[63,x] = F[61,x]
F[64,x] = F[65,x]+F[69,x]
F[65,x] = F[22,x]+F[54,x]+F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[43,x]+F[68,x]
F[68,x] = F[66,x]
F[69,x] = 2*F[22,x]+F[70,x]+F[83,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[72,x]+F[82,x]
F[72,x] = F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[34,x]+F[4,x]
F[77,x] = F[73,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[72,x]+F[81,x]
F[81,x] = F[78,x]
F[82,x] = F[70,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[48,x]+F[85,x]
F[85,x] = F[83,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[88,x]+F[90,x]
F[88,x] = F[43,x]+F[89,x]
F[89,x] = F[74,x]
F[90,x] = F[48,x]+F[91,x]
F[91,x] = F[70,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{42}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{21}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{14}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{39}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{31}\! \left(x \right)
F_{29}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{25}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{32}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{14}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{35}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{53}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)
F_{46}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{47}\! \left(x \right) = F_{43}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{43}\! \left(x \right)
F_{52}\! \left(x \right) = F_{48}\! \left(x \right)
F_{53}\! \left(x \right) = F_{22}\! \left(x \right)+F_{54}\! \left(x \right)+F_{86}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{64}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{60}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{1}\! \left(x \right)+F_{57}\! \left(x \right)
F_{60}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{14}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{61}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{69}\! \left(x \right)
F_{65}\! \left(x \right) = F_{22}\! \left(x \right)+F_{54}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{43}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{70}\! \left(x \right)+F_{83}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{82}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{77}\! \left(x \right)
F_{76}\! \left(x \right) = F_{34}\! \left(x \right)+F_{4}\! \left(x \right)
F_{77}\! \left(x \right) = F_{73}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{72}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{78}\! \left(x \right)
F_{82}\! \left(x \right) = F_{70}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{48}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{90}\! \left(x \right)
F_{88}\! \left(x \right) = F_{43}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{74}\! \left(x \right)
F_{90}\! \left(x \right) = F_{48}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{70}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_42(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_21(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_10(x) + F_17(x))
Eq(F_17(x), F_14(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_14(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_39(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_28(x))
Eq(F_25(x), F_26(x) + F_4(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_25(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_31(x))
Eq(F_29(x), F_22(x) + F_23(x) + F_30(x))
Eq(F_30(x), F_14(x)*F_4(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_25(x) + F_37(x))
Eq(F_37(x), F_34(x) + F_38(x))
Eq(F_38(x), F_32(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_14(x) + F_41(x))
Eq(F_41(x), F_35(x))
Eq(F_42(x), F_43(x) + F_53(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_47(x))
Eq(F_46(x), F_1(x) + F_14(x))
Eq(F_47(x), F_43(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_43(x))
Eq(F_52(x), F_48(x))
Eq(F_53(x), F_22(x) + F_54(x) + F_86(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_64(x))
Eq(F_56(x), F_57(x) + F_60(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_1(x) + F_57(x))
Eq(F_60(x), F_22(x) + F_23(x) + F_61(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_14(x) + F_63(x))
Eq(F_63(x), F_61(x))
Eq(F_64(x), F_65(x) + F_69(x))
Eq(F_65(x), F_22(x) + F_54(x) + F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_43(x) + F_68(x))
Eq(F_68(x), F_66(x))
Eq(F_69(x), 2*F_22(x) + F_70(x) + F_83(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_82(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_34(x) + F_4(x))
Eq(F_77(x), F_73(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_72(x) + F_81(x))
Eq(F_81(x), F_78(x))
Eq(F_82(x), F_70(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_48(x) + F_85(x))
Eq(F_85(x), F_83(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_90(x))
Eq(F_88(x), F_43(x) + F_89(x))
Eq(F_89(x), F_74(x))
Eq(F_90(x), F_48(x) + F_91(x))
Eq(F_91(x), F_70(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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[[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, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": 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