012_0321_1302_2031
Counting sequence:
1, 1, 2, 5, 11, 24, 53, 117, 258, 569, 1255, 2768, 6105, 13465, 29698, 65501, 144467, 318632, 702765, 1549997, 3418626, 7540017, 16630031, 36678688, 80897393, 178424817, 393528322, 867954037, 1914332891, 4222194104, 9312342245, 20539017381, 45300228866, 99912799977, 220364617335, 486029463536, 1071971727049, 2364308071433, 5214645606402, 11501262939853, 25366833951139, 55948313508680, 123397889957213, 272162613865565, 600273541239810, 1323944972436833, 2920052558739231, 6440378658718272, 14204702289873377, 31329457138485985, 69099292935690242, 152403288161253861, 336136033460993707, 741371359857677656, 1635146007876609173, 3606428049214212053, 7954227458286101762, 17543600924448812697, 38693629898111837447, 85341487254509776656, 188226575433468366009, 415146780765048569465, 915635048784606915586, 2019496673002682197181, 4454140126770412963827, 9823915302325432843240, 21667327277653547883661, 47788794682077508731149, 105401504666480450305538, 232470336610614448494737, 512729467903306405720623, 1130860440473093261746784, 2494191217556800971988305, 5501111903016908349697233, 12133084246506909961141250, 26760359710570620894270805, 59021831324158150138238843, 130176746894823210237618936, 287113853500217041369508677, 633249538324592232877256197, 1396675823544007675992131330, 3080465500588232393353771337, 6794180539501057019584798871, 14985036902546121715161729072, 33050539305680475823677229481, 72895259150862008666939257833, 160775555204270139049040244738, 354601649714220753921757718957, 782098558579303516510454695747, 1724972672362877172069949636232, 3804546994439975098061656991421, 8391192547459253712633768678589, 18507357767281384597337486993410, 40819262529002744292736630978241, 90029717605464742298107030635071, 198566792978210869193551548263552, 437952848485424482679839727505345, 965935414576313707657786485645761, 2130437622130838284509124519555074, 4698828092747101051698088766615493, 10363591600070515811053964018876747
Generating function in Maple syntax:
(x-1)/(x^3+2*x-1)
Generating function in latex syntax:
\frac{x -1}{x^{3}+2 x -1}
Generating function in sympy syntax:
(x - 1)/(x**3 + 2*x - 1)
Implicit equation for the generating function in Maple syntax:
(x^3+2*x-1)*F(x)+1-x = 0
Implicit equation for the generating function in latex syntax:
\left(x^{3}+2 x -1\right) F \! \left(x \right)+1-x = 0
Explicit closed form in Maple syntax:
-61/24060672*(3/8*2^(1/3)*((I*3^(2/3)+3^(1/6))*59^(1/2)-59/3*I*3^(1/6)-59/9*3^(2/3))*(9+59^(1/2)*3^(1/2))^(2/3)+236+(I*3^(1/3)-1/3*3^(5/6))*59^(1/2)*2^(2/3)*(9+59^(1/2)*3^(1/2))^(1/3))*((-3*I*59^(1/2)-9)*(108+12*59^(1/2)*3^(1/2))^(1/3)+9*3^(5/6)*(I+1/9*59^(1/2))*(36+4*59^(1/2)*3^(1/2))^(1/3)-48*I*3^(1/2)-48)^(-n)*(48/61*3^n*(I*59^(1/2)-767)*(-8*(108+12*59^(1/2)*3^(1/2))^(1/3)+8*I*(36+4*59^(1/2)*3^(1/2))^(1/3)*3^(5/6)+((I*59^(1/2)-3)*18^(1/3)-9*I*2^(1/3)*3^(1/6)+2^(1/3)*3^(1/6)*59^(1/2))*(9+59^(1/2)*3^(1/2))^(2/3))^n*(((I*59^(1/2)+3)*(81+9*59^(1/2)*3^(1/2))^(1/3)-9*3^(1/6)*(I+1/9*59^(1/2))*(9+59^(1/2)*3^(1/2))^(1/3)+8*I*3^(5/6)*2^(1/3)+8*6^(1/3))/((9+59^(1/2)*3^(1/2))^(1/3)*59^(1/2)*3^(1/6)-3*(81+9*59^(1/2)*3^(1/2))^(1/3)-8*6^(1/3)))^n+(-8*(108+12*59^(1/2)*3^(1/2))^(1/3)-8*I*(36+4*59^(1/2)*3^(1/2))^(1/3)*3^(5/6)+((-I*59^(1/2)-3)*18^(1/3)+9*I*2^(1/3)*3^(1/6)+2^(1/3)*3^(1/6)*59^(1/2))*(9+59^(1/2)*3^(1/2))^(2/3))^n*((I*59^(1/2)*3^(2/3)-1121/61*3^(2/3)-885/61*I*3^(1/6))*2^(1/3+2/3*n)*(9+59^(1/2)*3^(1/2))^(2/3-1/3*n)+84/61*(9+59^(1/2)*3^(1/2))^(1/3-1/3*n)*2^(2/3+2/3*n)*((I*3^(1/3)-38/21*3^(5/6))*59^(1/2)+59/21*I*3^(5/6)))*(1/((9+59^(1/2)*3^(1/2))^(1/3)*59^(1/2)*3^(1/6)-3*(81+9*59^(1/2)*3^(1/2))^(1/3)-8*6^(1/3)))^n*(12*(108+12*59^(1/2)*3^(1/2))^(1/3)-12*I*(36+4*59^(1/2)*3^(1/2))^(1/3)*3^(5/6)+1/2*((-3*I*59^(1/2)+9)*18^(1/3)+27*I*2^(1/3)*3^(1/6)-3*2^(1/3)*3^(1/6)*59^(1/2))*(9+59^(1/2)*3^(1/2))^(2/3))^n+171/61*59^(1/2)*3^(1/6)*2^(1/3+2/3*n)*(9+59^(1/2)*3^(1/2))^(2/3-1/3*n)*(-24*(108+12*59^(1/2)*3^(1/2))^(1/3)-24*I*(36+4*59^(1/2)*3^(1/2))^(1/3)*3^(5/6)+((-3*I*59^(1/2)-9)*18^(1/3)+27*I*2^(1/3)*3^(1/6)+3*2^(1/3)*3^(1/6)*59^(1/2))*(9+59^(1/2)*3^(1/2))^(2/3))^n*(4*(108+12*59^(1/2)*3^(1/2))^(1/3)-4*I*(36+4*59^(1/2)*3^(1/2))^(1/3)*3^(5/6)+1/2*((-I*59^(1/2)+3)*18^(1/3)+9*I*2^(1/3)*3^(1/6)-2^(1/3)*3^(1/6)*59^(1/2))*(9+59^(1/2)*3^(1/2))^(2/3))^n*(1/((9+59^(1/2)*3^(1/2))^(1/3)*59^(1/2)*3^(1/6)-3*(81+9*59^(1/2)*3^(1/2))^(1/3)-8*6^(1/3)))^n+(116/61*2^(1/3)*((I*3^(2/3)+3/58*3^(1/6))*59^(1/2)-531/29*I*3^(1/6)+59/58*3^(2/3))*(9+59^(1/2)*3^(1/2))^(2/3)+270/61*((I*3^(1/3)+17/135*3^(5/6))*59^(1/2)+59/135*I*3^(5/6)-59/45*3^(1/3))*2^(2/3)*(9+59^(1/2)*3^(1/2))^(1/3)-48/61*I*59^(1/2)-36816/61)*(-48*(108+12*59^(1/2)*3^(1/2))^(1/3)+48*I*(36+4*59^(1/2)*3^(1/2))^(1/3)*3^(5/6)+((6*I*59^(1/2)-18)*18^(1/3)-54*I*2^(1/3)*3^(1/6)+6*2^(1/3)*3^(1/6)*59^(1/2))*(9+59^(1/2)*3^(1/2))^(2/3))^n-33984/61*(-48*(108+12*59^(1/2)*3^(1/2))^(1/3)-48*I*(36+4*59^(1/2)*3^(1/2))^(1/3)*3^(5/6)+((-6*I*59^(1/2)-18)*18^(1/3)+54*I*2^(1/3)*3^(1/6)+6*2^(1/3)*3^(1/6)*59^(1/2))*(9+59^(1/2)*3^(1/2))^(2/3))^n)*(108+12*59^(1/2)*3^(1/2))^(-2/3*n)*(1/576*(3*I*59^(1/2)-9)*(108+12*59^(1/2)*3^(1/2))^(1/3)-1/64*3^(5/6)*(I-1/9*59^(1/2))*(36+4*59^(1/2)*3^(1/2))^(1/3)+1/12*I*3^(1/2)-1/12)^(-n)
Explicit closed form in latex syntax:
-\frac{61 \left(\frac{3 \,2^{\frac{1}{3}} \left(\left(i 3^{\frac{2}{3}}+3^{\frac{1}{6}}\right) \sqrt{59}-\frac{59 i 3^{\frac{1}{6}}}{3}-\frac{59 \,3^{\frac{2}{3}}}{9}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}}{8}+236+\left(i 3^{\frac{1}{3}}-\frac{3^{\frac{5}{6}}}{3}\right) \sqrt{59}\, 2^{\frac{2}{3}} \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\left(-3 i \sqrt{59}-9\right) \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}+9 \,3^{\frac{5}{6}} \left(i+\frac{\sqrt{59}}{9}\right) \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}-48 i \sqrt{3}-48\right)^{-n} \left(\frac{48 \,3^{n} \left(i \sqrt{59}-767\right) \left(-8 \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}+8 i \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} 3^{\frac{5}{6}}+\left(\left(i \sqrt{59}-3\right) 18^{\frac{1}{3}}-9 i 2^{\frac{1}{3}} 3^{\frac{1}{6}}+2^{\frac{1}{3}} 3^{\frac{1}{6}} \sqrt{59}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}\right)^{n} \left(\frac{\left(i \sqrt{59}+3\right) \left(81+9 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}-9 \,3^{\frac{1}{6}} \left(i+\frac{\sqrt{59}}{9}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}+8 i 3^{\frac{5}{6}} 2^{\frac{1}{3}}+8 \,6^{\frac{1}{3}}}{\left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} \sqrt{59}\, 3^{\frac{1}{6}}-3 \left(81+9 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}-8 \,6^{\frac{1}{3}}}\right)^{n}}{61}+\left(-8 \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}-8 i \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} 3^{\frac{5}{6}}+\left(\left(-i \sqrt{59}-3\right) 18^{\frac{1}{3}}+9 i 2^{\frac{1}{3}} 3^{\frac{1}{6}}+2^{\frac{1}{3}} 3^{\frac{1}{6}} \sqrt{59}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}\right)^{n} \left(\left(i \sqrt{59}\, 3^{\frac{2}{3}}-\frac{1121 \,3^{\frac{2}{3}}}{61}-\frac{885 i 3^{\frac{1}{6}}}{61}\right) 2^{\frac{1}{3}+\frac{2 n}{3}} \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}-\frac{n}{3}}+\frac{84 \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}-\frac{n}{3}} 2^{\frac{2}{3}+\frac{2 n}{3}} \left(\left(i 3^{\frac{1}{3}}-\frac{38 \,3^{\frac{5}{6}}}{21}\right) \sqrt{59}+\frac{59 i 3^{\frac{5}{6}}}{21}\right)}{61}\right) \left(\frac{1}{\left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} \sqrt{59}\, 3^{\frac{1}{6}}-3 \left(81+9 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}-8 \,6^{\frac{1}{3}}}\right)^{n} \left(12 \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}-12 i \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} 3^{\frac{5}{6}}+\frac{\left(\left(-3 i \sqrt{59}+9\right) 18^{\frac{1}{3}}+27 i 2^{\frac{1}{3}} 3^{\frac{1}{6}}-3 \,2^{\frac{1}{3}} 3^{\frac{1}{6}} \sqrt{59}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}}{2}\right)^{n}+\frac{171 \sqrt{59}\, 3^{\frac{1}{6}} 2^{\frac{1}{3}+\frac{2 n}{3}} \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}-\frac{n}{3}} \left(-24 \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}-24 i \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} 3^{\frac{5}{6}}+\left(\left(-3 i \sqrt{59}-9\right) 18^{\frac{1}{3}}+27 i 2^{\frac{1}{3}} 3^{\frac{1}{6}}+3 \,2^{\frac{1}{3}} 3^{\frac{1}{6}} \sqrt{59}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}\right)^{n} \left(4 \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}-4 i \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} 3^{\frac{5}{6}}+\frac{\left(\left(-i \sqrt{59}+3\right) 18^{\frac{1}{3}}+9 i 2^{\frac{1}{3}} 3^{\frac{1}{6}}-2^{\frac{1}{3}} 3^{\frac{1}{6}} \sqrt{59}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}}{2}\right)^{n} \left(\frac{1}{\left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} \sqrt{59}\, 3^{\frac{1}{6}}-3 \left(81+9 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}-8 \,6^{\frac{1}{3}}}\right)^{n}}{61}+\left(\frac{116 \,2^{\frac{1}{3}} \left(\left(i 3^{\frac{2}{3}}+\frac{3 \,3^{\frac{1}{6}}}{58}\right) \sqrt{59}-\frac{531 i 3^{\frac{1}{6}}}{29}+\frac{59 \,3^{\frac{2}{3}}}{58}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}}{61}+\frac{270 \left(\left(i 3^{\frac{1}{3}}+\frac{17 \,3^{\frac{5}{6}}}{135}\right) \sqrt{59}+\frac{59 i 3^{\frac{5}{6}}}{135}-\frac{59 \,3^{\frac{1}{3}}}{45}\right) 2^{\frac{2}{3}} \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{61}-\frac{48 i \sqrt{59}}{61}-\frac{36816}{61}\right) \left(-48 \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}+48 i \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} 3^{\frac{5}{6}}+\left(\left(6 i \sqrt{59}-18\right) 18^{\frac{1}{3}}-54 i 2^{\frac{1}{3}} 3^{\frac{1}{6}}+6 \,2^{\frac{1}{3}} 3^{\frac{1}{6}} \sqrt{59}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}\right)^{n}-\frac{33984 \left(-48 \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}-48 i \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} 3^{\frac{5}{6}}+\left(\left(-6 i \sqrt{59}-18\right) 18^{\frac{1}{3}}+54 i 2^{\frac{1}{3}} 3^{\frac{1}{6}}+6 \,2^{\frac{1}{3}} 3^{\frac{1}{6}} \sqrt{59}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}\right)^{n}}{61}\right) \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{-\frac{2 n}{3}} \left(\frac{\left(3 i \sqrt{59}-9\right) \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{576}-\frac{3^{\frac{5}{6}} \left(i-\frac{\sqrt{59}}{9}\right) \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{64}+\frac{i \sqrt{3}}{12}-\frac{1}{12}\right)^{-n}}{24060672}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(n) = -2*a(n+2)+a(n+3), n >= 3
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(n \right) = -2 a \! \left(n +2\right)+a \! \left(n +3\right), \quad n \geq 3
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/545/
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[10,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[1,x]+F[4,x]
F[10,x] = F[11,x]+F[2,x]
F[11,x] = F[12,x]+F[13,x]+F[17,x]
F[12,x] = 0
F[13,x] = F[14,x]*F[4,x]
F[14,x] = F[15,x]+F[16,x]
F[15,x] = F[7,x]
F[16,x] = F[11,x]
F[17,x] = F[18,x]*F[4,x]
F[18,x] = F[19,x]+F[2,x]
F[19,x] = F[20,x]
F[20,x] = F[2,x]*F[4,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_{10}\! \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_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{13}\! \left(x \right)+F_{17}\! \left(x \right)
F_{12}\! \left(x \right) = 0
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)
F_{15}\! \left(x \right) = F_{7}\! \left(x \right)
F_{16}\! \left(x \right) = F_{11}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \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_10(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_1(x) + F_4(x))
Eq(F_10(x), F_11(x) + F_2(x))
Eq(F_11(x), F_12(x) + F_13(x) + F_17(x))
Eq(F_12(x), 0)
Eq(F_13(x), F_14(x)*F_4(x))
Eq(F_14(x), F_15(x) + F_16(x))
Eq(F_15(x), F_7(x))
Eq(F_16(x), F_11(x))
Eq(F_17(x), F_18(x)*F_4(x))
Eq(F_18(x), F_19(x) + F_2(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_2(x)*F_4(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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", 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