0132_0231_1230_2130
Counting sequence:
1, 1, 2, 6, 20, 68, 228, 748, 2404, 7596, 23684, 73100, 223908, 681964, 2068420, 6254412, 18869732, 56838572, 171007236, 514070284, 1544439076, 4638035820, 13924068932, 41793178316, 125423575140, 376363000108, 1129281938308, 3388248468108, 10165584265124, 30498497625836, 91499116756164, 274504866461260, 823530168640228, 2470622718175404, 7411934726519300, 22235941618511372, 66708108323375652, 200124909085679212, 600375929847880516, 1801130263444804044, 5403395875575690596, 16210198072087535660, 48630615656739348612, 145891890950683156876, 437675763012002948260, 1313027473753962311148, 3939082799493886888388, 11817249172537846619468, 35451749100910283855844, 106355250539693083740076, 319065758233741203920644, 957197288212022493873420, 2871591892220615199264548, 8614775732956840939924844, 25844327313712313317722180, 77532982175324120576432332, 232598947003353922230569572, 697796841982839286203735852, 2093390527930101694654225796, 6280171587825530350086641804, 18840514771691156770583710116, 56521544331790832128550411500, 169564633029383680771553220292, 508693899157326332591070479436, 1526081697612635421335246769380, 4578245093123830797148238358188, 13734735279952564829766565950468, 41204205841038286110017109154828, 123612617525512935059633569174564, 370837852581408745614360029150316, 1112513557754113691666588407117124, 3337540673282411132551961213509580, 10012622019887963808570634330496868, 30037866059746532839162121782730284, 90113598179407242527628237753277060, 270340794538561737969651327715217292, 811022383616374679415452951346851492, 2433067150850521858725288269023808492, 7299201452554398996065586594199643076, 21897604357668939385839929271178783564, 65692813073018454068533578619342897636, 197078439219078936259083221126935463340, 591235317657284561347124441233207283972, 1773705952971950398106942494033598345996, 5321117858916047040303605052027097438500, 15963353576748537648579648754450595941228, 47890060730246415672483170377123792724548, 143670182190740871813751073192982183274188, 431010546572225903719482571370301750621284, 1293031639716684365086158873029882834656556, 3879094919150066557856403847600138031945604, 11637284757450226908250075821166461876569740, 34911854272350735813081975662921618640737188, 104735562817052318853849462672989596843391724, 314206688451157181866635537958178822170783940, 942620065353472001161841070894477629390066252, 2827860196060416924512912441006357413118621412, 8483580588181252635400556408231005687638697132, 25450741764543761669539388652249052756253732356, 76352225293631292614521767326123567248980429324, 229056675880893893213828829745652194894467653156
Generating function in Maple syntax:
(x-1)*(2*x^3+6*x^2-5*x+1)/(3*x-1)/(2*x-1)^2
Generating function in latex syntax:
\frac{\left(x -1\right) \left(2 x^{3}+6 x^{2}-5 x +1\right)}{\left(3 x -1\right) \left(2 x -1\right)^{2}}
Generating function in sympy syntax:
(x - 1)*(2*x**3 + 6*x**2 - 5*x + 1)/((2*x - 1)**2*(3*x - 1))
Implicit equation for the generating function in Maple syntax:
-(3*x-1)*(2*x-1)^2*F(x)+(x-1)*(2*x^3+6*x^2-5*x+1) = 0
Implicit equation for the generating function in latex syntax:
-\left(3 x -1\right) \left(2 x -1\right)^{2} F \! \left(x \right)+\left(x -1\right) \left(2 x^{3}+6 x^{2}-5 x +1\right) = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,-1/4*2^n*n+4/9*3^n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ -\frac{2^{n} n}{4}+\frac{4 \,3^{n}}{9} & \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(n+3) = 12*a(n)-16*a(n+1)+7*a(n+2), n >= 5
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(n +3\right) = 12 a \! \left(n \right)-16 a \! \left(n +1\right)+7 a \! \left(n +2\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15352/
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[12,x]*F[4,x]
F[4,x] = F[22,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[14,x]+F[17,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[1,x]+F[14,x]
F[17,x] = F[18,x]+F[19,x]+F[21,x]
F[18,x] = 0
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[10,x]+F[17,x]
F[21,x] = F[12,x]*F[13,x]
F[22,x] = F[23,x]+F[29,x]
F[23,x] = F[24,x]
F[24,x] = F[12,x]*F[25,x]
F[25,x] = F[16,x]+F[26,x]
F[26,x] = F[23,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[12,x]*F[26,x]
F[29,x] = F[18,x]+F[30,x]+F[66,x]
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[32,x]+F[44,x]
F[32,x] = F[33,x]+F[6,x]
F[33,x] = F[18,x]+F[19,x]+F[34,x]
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[13,x]+F[36,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[38,x]
F[38,x] = F[12,x]*F[39,x]
F[39,x] = F[14,x]+F[37,x]
F[40,x] = 2*F[18,x]+F[41,x]+F[43,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[17,x]+F[40,x]
F[43,x] = F[12,x]*F[36,x]
F[44,x] = F[29,x]+F[45,x]
F[45,x] = 2*F[18,x]+F[46,x]+F[56,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[48,x]+F[53,x]
F[48,x] = F[18,x]+F[49,x]+F[51,x]
F[49,x] = F[12,x]*F[50,x]
F[50,x] = F[20,x]+F[47,x]
F[51,x] = F[12,x]*F[52,x]
F[52,x] = F[23,x]+F[48,x]
F[53,x] = 2*F[18,x]+F[46,x]+F[54,x]
F[54,x] = F[12,x]*F[55,x]
F[55,x] = F[27,x]+F[53,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[55,x]+F[58,x]
F[58,x] = F[59,x]+F[62,x]
F[59,x] = F[60,x]
F[60,x] = F[12,x]*F[61,x]
F[61,x] = F[27,x]+F[59,x]
F[62,x] = 3*F[18,x]+F[63,x]+F[65,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[53,x]+F[62,x]
F[65,x] = F[12,x]*F[58,x]
F[66,x] = F[12,x]*F[67,x]
F[67,x] = F[52,x]+F[68,x]
F[68,x] = F[69,x]+F[79,x]
F[69,x] = F[18,x]+F[70,x]+F[77,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[14,x]+F[37,x]
F[73,x] = F[27,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[12,x]*F[76,x]
F[76,x] = F[27,x]+F[74,x]
F[77,x] = F[12,x]*F[78,x]
F[78,x] = F[23,x]+F[69,x]
F[79,x] = F[18,x]+F[80,x]+F[89,x]+F[91,x]
F[80,x] = F[12,x]*F[81,x]
F[81,x] = F[82,x]+F[83,x]
F[82,x] = F[17,x]+F[40,x]
F[83,x] = F[53,x]+F[84,x]
F[84,x] = 3*F[18,x]+F[85,x]+F[87,x]
F[85,x] = F[12,x]*F[86,x]
F[86,x] = F[53,x]+F[84,x]
F[87,x] = F[12,x]*F[88,x]
F[88,x] = F[74,x]+F[84,x]
F[89,x] = F[12,x]*F[90,x]
F[90,x] = F[48,x]+F[79,x]
F[91,x] = F[12,x]*F[68,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{22}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \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_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
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_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{29}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{16}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{23}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{29}\! \left(x \right) = F_{18}\! \left(x \right)+F_{30}\! \left(x \right)+F_{66}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{44}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{6}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{13}\! \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_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{14}\! \left(x \right)+F_{37}\! \left(x \right)
F_{40}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{41}\! \left(x \right)+F_{43}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{17}\! \left(x \right)+F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{44}\! \left(x \right) = F_{29}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{46}\! \left(x \right)+F_{56}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{53}\! \left(x \right)
F_{48}\! \left(x \right) = F_{18}\! \left(x \right)+F_{49}\! \left(x \right)+F_{51}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{20}\! \left(x \right)+F_{47}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{23}\! \left(x \right)+F_{48}\! \left(x \right)
F_{53}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{46}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{27}\! \left(x \right)+F_{53}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{55}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{62}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{27}\! \left(x \right)+F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{63}\! \left(x \right)+F_{65}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{53}\! \left(x \right)+F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{52}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{79}\! \left(x \right)
F_{69}\! \left(x \right) = F_{18}\! \left(x \right)+F_{70}\! \left(x \right)+F_{77}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{14}\! \left(x \right)+F_{37}\! \left(x \right)
F_{73}\! \left(x \right) = F_{27}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{27}\! \left(x \right)+F_{74}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{23}\! \left(x \right)+F_{69}\! \left(x \right)
F_{79}\! \left(x \right) = F_{18}\! \left(x \right)+F_{80}\! \left(x \right)+F_{89}\! \left(x \right)+F_{91}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{83}\! \left(x \right)
F_{82}\! \left(x \right) = F_{17}\! \left(x \right)+F_{40}\! \left(x \right)
F_{83}\! \left(x \right) = F_{53}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{85}\! \left(x \right)+F_{87}\! \left(x \right)
F_{85}\! \left(x \right) = F_{12}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{53}\! \left(x \right)+F_{84}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{74}\! \left(x \right)+F_{84}\! \left(x \right)
F_{89}\! \left(x \right) = F_{12}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{48}\! \left(x \right)+F_{79}\! \left(x \right)
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_22(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_1(x) + F_14(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_21(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_10(x) + F_17(x))
Eq(F_21(x), F_12(x)*F_13(x))
Eq(F_22(x), F_23(x) + F_29(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_12(x)*F_25(x))
Eq(F_25(x), F_16(x) + F_26(x))
Eq(F_26(x), F_23(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_12(x)*F_26(x))
Eq(F_29(x), F_18(x) + F_30(x) + F_66(x))
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_44(x))
Eq(F_32(x), F_33(x) + F_6(x))
Eq(F_33(x), F_18(x) + F_19(x) + F_34(x))
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_13(x) + F_36(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_12(x)*F_39(x))
Eq(F_39(x), F_14(x) + F_37(x))
Eq(F_40(x), 2*F_18(x) + F_41(x) + F_43(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_17(x) + F_40(x))
Eq(F_43(x), F_12(x)*F_36(x))
Eq(F_44(x), F_29(x) + F_45(x))
Eq(F_45(x), 2*F_18(x) + F_46(x) + F_56(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_53(x))
Eq(F_48(x), F_18(x) + F_49(x) + F_51(x))
Eq(F_49(x), F_12(x)*F_50(x))
Eq(F_50(x), F_20(x) + F_47(x))
Eq(F_51(x), F_12(x)*F_52(x))
Eq(F_52(x), F_23(x) + F_48(x))
Eq(F_53(x), 2*F_18(x) + F_46(x) + F_54(x))
Eq(F_54(x), F_12(x)*F_55(x))
Eq(F_55(x), F_27(x) + F_53(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_55(x) + F_58(x))
Eq(F_58(x), F_59(x) + F_62(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_12(x)*F_61(x))
Eq(F_61(x), F_27(x) + F_59(x))
Eq(F_62(x), 3*F_18(x) + F_63(x) + F_65(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_53(x) + F_62(x))
Eq(F_65(x), F_12(x)*F_58(x))
Eq(F_66(x), F_12(x)*F_67(x))
Eq(F_67(x), F_52(x) + F_68(x))
Eq(F_68(x), F_69(x) + F_79(x))
Eq(F_69(x), F_18(x) + F_70(x) + F_77(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_14(x) + F_37(x))
Eq(F_73(x), F_27(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_12(x)*F_76(x))
Eq(F_76(x), F_27(x) + F_74(x))
Eq(F_77(x), F_12(x)*F_78(x))
Eq(F_78(x), F_23(x) + F_69(x))
Eq(F_79(x), F_18(x) + F_80(x) + F_89(x) + F_91(x))
Eq(F_80(x), F_12(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_83(x))
Eq(F_82(x), F_17(x) + F_40(x))
Eq(F_83(x), F_53(x) + F_84(x))
Eq(F_84(x), 3*F_18(x) + F_85(x) + F_87(x))
Eq(F_85(x), F_12(x)*F_86(x))
Eq(F_86(x), F_53(x) + F_84(x))
Eq(F_87(x), F_12(x)*F_88(x))
Eq(F_88(x), F_74(x) + F_84(x))
Eq(F_89(x), F_12(x)*F_90(x))
Eq(F_90(x), F_48(x) + F_79(x))
Eq(F_91(x), F_12(x)*F_68(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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