0213_1302_2130_2301
Counting sequence:
1, 1, 2, 6, 20, 64, 195, 572, 1631, 4553, 12509, 33959, 91368, 244183, 649304, 1720032, 4543466, 11975794, 31514865, 82830806, 217501685, 570722651, 1496763227, 3923761121, 10282908510, 26941741369, 70575869750, 184852976442, 484117276976, 1267767289588, 3319721462319, 8692470838784, 22759838537243, 59591339739773, 156022770616169, 408494151977387, 1069494045053796, 2800056702660139, 7330813501879460, 19192658680884516, 50247712296587270, 131551577720504326, 344409219888180477, 901680479990547386, 2360641016176483025, 6180260160724945199, 16180174650370440455, 42360334159130552837, 110900968564509572346, 290342853009374873773, 760128153413568469154, 1990042733131237375134, 5210002297779957340268, 13639968663808262014888, 35709912700844083444059, 93489787453122497797892, 244759485687320428912151, 640788741666432826865009, 1677606883427166127537205, 4392032196845441707456751, 11498490283569911298254880, 30103439806785796794153151, 78811831442630488297896752, 206332059132791686526923176, 540184355179116608137646690, 1414221024851302211595566554, 3702478756268278174068154185, 9693215317740508605447100382, 25377167344527200231949557741, 66438287010988997269754396483, 173937694278735601936019281139, 455374797005809429255714748009, 1192186699099875927265947567318, 3121185305016184835411773165153, 8171369225393411544708662352974, 21392922390053515730192794745922, 56007397982546067508826883591656, 146629271633142550522202179445404, 383880417067997311509608301579975, 1005011979873080838910280018968136, 2631155523155708115028546342674515, 6888454590802969325789988183758501, 18034208251671051501570676558010177, 47214170169045888457380558189093491, 123608302265138020427488031406916380, 323610736645710985938917602826951059, 847223907710680563616932910664530940, 2218060986563701957367217396347833452, 5806959052135167813395391812741356286, 15202816170151286492640303110601012718, 39801489458937661684168207656511240149, 104201652207899638599149700133831828034, 272803467167237134191851653294782488393, 714208749298763524133546780850112129943, 1869822780738956958523071731454746891039, 4895259592937914392064234497912514526477, 12815955998114400298926763931079568659186, 33552608401484514667230321632919735396949, 87841869206497600027792729642866725427770, 229972999218325198066204924646054616683046, 602077128449111819470936158996045476219300
Generating function in Maple syntax:
(2*x^6-5*x^5+15*x^4-24*x^3+19*x^2-7*x+1)/(2*x-1)/(x^2-3*x+1)/(x-1)^3
Generating function in latex syntax:
\frac{2 x^{6}-5 x^{5}+15 x^{4}-24 x^{3}+19 x^{2}-7 x +1}{\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(2*x**6 - 5*x**5 + 15*x**4 - 24*x**3 + 19*x**2 - 7*x + 1)/((x - 1)**3*(2*x - 1)*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x^2-3*x+1)*(x-1)^3*F(x)-2*x^6+5*x^5-15*x^4+24*x^3-19*x^2+7*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x -1\right)^{3} F \! \left(x \right)-2 x^{6}+5 x^{5}-15 x^{4}+24 x^{3}-19 x^{2}+7 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/10*(11*5^(1/2)-15)*(3/2-1/2*5^(1/2))^(-n)+1/10*(-11*5^(1/2)-15)*(3/2+1/2*5^(1/2))^(-n)+1/2*n^2-3/2*n-2^(n+1)+5)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(11 \sqrt{5}-15\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{10}+\frac{\left(-11 \sqrt{5}-15\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{10}+\frac{n^{2}}{2}-\frac{3 n}{2}-\\2^{n +1}+5 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 64
a(6) = 195
a(n+3) = 1/2*n^2+2*a(n)-7*a(n+1)+5*a(n+2)-3/2*n+3, 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) = 20
a \! \left(5\right) = 64
a \! \left(6\right) = 195
a \! \left(n +3\right) = \frac{n^{2}}{2}+2 a \! \left(n \right)-7 a \! \left(n +1\right)+5 a \! \left(n +2\right)-\frac{3 n}{2}+3, \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/21397/
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[11,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[11,x]*F[7,x]*F[78,x]
F[7,x] = F[74,x]+F[8,x]
F[8,x] = F[12,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]*F[9,x]
F[11,x] = x
F[12,x] = F[13,x]+F[23,x]
F[13,x] = F[14,x]
F[14,x] = F[11,x]*F[15,x]
F[15,x] = F[16,x]+F[18,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[11,x]*F[16,x]
F[18,x] = F[19,x]
F[19,x] = F[11,x]*F[16,x]*F[20,x]
F[20,x] = F[15,x]+F[21,x]
F[21,x] = F[22,x]*F[9,x]
F[22,x] = F[17,x]
F[23,x] = F[24,x]+F[25,x]+F[31,x]
F[24,x] = 0
F[25,x] = F[11,x]*F[26,x]
F[26,x] = F[27,x]+F[33,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[10,x]
F[29,x] = F[24,x]+F[30,x]+F[31,x]
F[30,x] = F[11,x]*F[27,x]
F[31,x] = F[11,x]*F[32,x]
F[32,x] = F[22,x]+F[29,x]
F[33,x] = F[34,x]+F[52,x]
F[34,x] = F[24,x]+F[35,x]+F[47,x]
F[35,x] = F[11,x]*F[36,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[28,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[11,x]*F[37,x]
F[40,x] = F[34,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[11,x]*F[43,x]
F[43,x] = F[44,x]+F[51,x]
F[44,x] = F[24,x]+F[45,x]+F[47,x]
F[45,x] = F[11,x]*F[46,x]
F[46,x] = F[28,x]+F[44,x]
F[47,x] = F[11,x]*F[48,x]
F[48,x] = F[11,x]+F[49,x]
F[49,x] = F[24,x]+F[47,x]+F[50,x]
F[50,x] = F[11,x]*F[28,x]
F[51,x] = F[42,x]
F[52,x] = F[24,x]+F[53,x]+F[65,x]+F[67,x]
F[53,x] = F[11,x]*F[54,x]
F[54,x] = F[55,x]+F[58,x]
F[55,x] = F[29,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[11,x]*F[55,x]
F[58,x] = F[52,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[11,x]*F[61,x]
F[61,x] = F[62,x]+F[73,x]
F[62,x] = F[24,x]+F[63,x]+F[65,x]+F[67,x]
F[63,x] = F[11,x]*F[64,x]
F[64,x] = F[29,x]+F[62,x]
F[65,x] = F[11,x]*F[66,x]
F[66,x] = F[44,x]+F[62,x]
F[67,x] = F[11,x]*F[68,x]
F[68,x] = F[69,x]+F[71,x]
F[69,x] = F[70,x]
F[70,x] = F[11,x]*F[22,x]
F[71,x] = 2*F[24,x]+F[67,x]+F[72,x]
F[72,x] = F[11,x]*F[29,x]
F[73,x] = F[60,x]
F[74,x] = F[75,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[13,x]*F[9,x]
F[77,x] = F[22,x]*F[28,x]
F[78,x] = F[1,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[11,x]*F[81,x]
F[81,x] = F[78,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[11,x]*F[81,x]*F[9,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_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right) F_{78}\! \left(x \right)
F_{7}\! \left(x \right) = F_{74}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{12}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{9}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{23}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{18}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{9}\! \left(x \right)
F_{22}\! \left(x \right) = F_{17}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)+F_{31}\! \left(x \right)
F_{24}\! \left(x \right) = 0
F_{25}\! \left(x \right) = F_{11}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{33}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{10}\! \left(x \right)
F_{29}\! \left(x \right) = F_{24}\! \left(x \right)+F_{30}\! \left(x \right)+F_{31}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{27}\! \left(x \right)
F_{31}\! \left(x \right) = F_{11}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{22}\! \left(x \right)+F_{29}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{52}\! \left(x \right)
F_{34}\! \left(x \right) = F_{24}\! \left(x \right)+F_{35}\! \left(x \right)+F_{47}\! \left(x \right)
F_{35}\! \left(x \right) = F_{11}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{28}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{11}\! \left(x \right) F_{37}\! \left(x \right)
F_{40}\! \left(x \right) = F_{34}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{11}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{51}\! \left(x \right)
F_{44}\! \left(x \right) = F_{24}\! \left(x \right)+F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{45}\! \left(x \right) = F_{11}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{28}\! \left(x \right)+F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{11}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{24}\! \left(x \right)+F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right) F_{28}\! \left(x \right)
F_{51}\! \left(x \right) = F_{42}\! \left(x \right)
F_{52}\! \left(x \right) = F_{24}\! \left(x \right)+F_{53}\! \left(x \right)+F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{58}\! \left(x \right)
F_{55}\! \left(x \right) = F_{29}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{11}\! \left(x \right) F_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{52}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{11}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{73}\! \left(x \right)
F_{62}\! \left(x \right) = F_{24}\! \left(x \right)+F_{63}\! \left(x \right)+F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{63}\! \left(x \right) = F_{11}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{29}\! \left(x \right)+F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{11}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{44}\! \left(x \right)+F_{62}\! \left(x \right)
F_{67}\! \left(x \right) = F_{11}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{71}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{11}\! \left(x \right) F_{22}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{67}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{11}\! \left(x \right) F_{29}\! \left(x \right)
F_{73}\! \left(x \right) = F_{60}\! \left(x \right)
F_{74}\! \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_{13}\! \left(x \right) F_{9}\! \left(x \right)
F_{77}\! \left(x \right) = F_{22}\! \left(x \right) F_{28}\! \left(x \right)
F_{78}\! \left(x \right) = F_{1}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{11}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{78}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{11}\! \left(x \right) F_{81}\! \left(x \right) F_{9}\! \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_11(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_11(x)*F_7(x)*F_78(x))
Eq(F_7(x), F_74(x) + F_8(x))
Eq(F_8(x), F_12(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x)*F_9(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x) + F_23(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_11(x)*F_15(x))
Eq(F_15(x), F_16(x) + F_18(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_11(x)*F_16(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_11(x)*F_16(x)*F_20(x))
Eq(F_20(x), F_15(x) + F_21(x))
Eq(F_21(x), F_22(x)*F_9(x))
Eq(F_22(x), F_17(x))
Eq(F_23(x), F_24(x) + F_25(x) + F_31(x))
Eq(F_24(x), 0)
Eq(F_25(x), F_11(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_33(x))
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_10(x))
Eq(F_29(x), F_24(x) + F_30(x) + F_31(x))
Eq(F_30(x), F_11(x)*F_27(x))
Eq(F_31(x), F_11(x)*F_32(x))
Eq(F_32(x), F_22(x) + F_29(x))
Eq(F_33(x), F_34(x) + F_52(x))
Eq(F_34(x), F_24(x) + F_35(x) + F_47(x))
Eq(F_35(x), F_11(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_28(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_11(x)*F_37(x))
Eq(F_40(x), F_34(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_11(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_51(x))
Eq(F_44(x), F_24(x) + F_45(x) + F_47(x))
Eq(F_45(x), F_11(x)*F_46(x))
Eq(F_46(x), F_28(x) + F_44(x))
Eq(F_47(x), F_11(x)*F_48(x))
Eq(F_48(x), F_11(x) + F_49(x))
Eq(F_49(x), F_24(x) + F_47(x) + F_50(x))
Eq(F_50(x), F_11(x)*F_28(x))
Eq(F_51(x), F_42(x))
Eq(F_52(x), F_24(x) + F_53(x) + F_65(x) + F_67(x))
Eq(F_53(x), F_11(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_58(x))
Eq(F_55(x), F_29(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_11(x)*F_55(x))
Eq(F_58(x), F_52(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_11(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_73(x))
Eq(F_62(x), F_24(x) + F_63(x) + F_65(x) + F_67(x))
Eq(F_63(x), F_11(x)*F_64(x))
Eq(F_64(x), F_29(x) + F_62(x))
Eq(F_65(x), F_11(x)*F_66(x))
Eq(F_66(x), F_44(x) + F_62(x))
Eq(F_67(x), F_11(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_71(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_11(x)*F_22(x))
Eq(F_71(x), 2*F_24(x) + F_67(x) + F_72(x))
Eq(F_72(x), F_11(x)*F_29(x))
Eq(F_73(x), F_60(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_13(x)*F_9(x))
Eq(F_77(x), F_22(x)*F_28(x))
Eq(F_78(x), F_1(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_11(x)*F_81(x))
Eq(F_81(x), F_78(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_11(x)*F_81(x)*F_9(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": 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:
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"BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": 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