0231_2031_2301_3012
Counting sequence:
1, 1, 2, 6, 20, 67, 222, 730, 2393, 7839, 25682, 84157, 275808, 903949, 2962679, 9710103, 31824485, 104303296, 341849052, 1120393786, 3672036893, 12034925610, 39443895434, 129275489749, 423694264317, 1388637781858, 4551194220281, 14916322377630, 48887536429895, 160226573125327, 525134965086309, 1721104846609885, 5640839193712514, 18487581899529882, 60592169490078932, 198587950737123007, 650862553855482018, 2133171032979694630, 6991366501250499845, 22913870851945596687, 75099120797877776858, 246133792978735915309, 806691788165532233580, 2643893929469181173149, 8665236479201161973759, 28399900012461444588219, 93079320184019120048105, 305063040437382623421904, 999829591115538704503296, 3276893883431466732721426, 10739863691461487439785633, 35199391928550101725327230, 115364331218162279020961582, 378101103122154415061320417, 1239208364254645798775626149, 4061446415676156575972507602, 13311197263690401599139171665, 43626815291463171224512865154, 142984810064167993096777836119, 468625907541015851749126000375, 1535899100891102872005645970521, 5033836179685885421435381420473, 16498158420180748454494589372354, 54071928752032949706557686863054, 177218172143900147805183306423716, 580824121921936067087541935020123, 1903623406816634830271702720412678, 6239035085163378953317056412306306, 20448140453890252051189317194835905, 67017806810598139799057330340818847, 219647671133253078175744688081013554, 719884784809643427168911484302531197, 2359388108813732406540595331007524136, 7732782197200662753752653752283463005, 25343825496945506108359570804695290903, 83063181457787209795565393988945361263, 272235622626143278544734919559424197389, 892239292138211732652322107083998660096, 2924271800860373842803254229255214693092, 9584161604017916699597048023710134324890, 31411633359424913307484575810443942301125, 102950132841383956522621708778697407551794, 337414158976820741613073108519902971191778, 1105858841905937267690517335618801898866845, 3624399704890723488612611780608315395066093, 11878797476693970007565401723607110044448594, 38932193185509985901797540340589987499858409, 127598409620812421891667598940089668114893814, 418197712627716200145816693171311422994798231, 1370623092927076073071965710322461052955160335, 4492151932302268719784944911198245628557639965, 14722814088731140377775061771384097784482014869, 48253322229074305832585204427958776477722778626, 158147966286215878160628982203356804207821051938, 518322430147539336968922284836265846257882211780, 1698777087704269426911097985970707674954945167703, 5567661026916296260108683688742104411487947700298, 18247743941810829509895184487392988265681585363118, 59806112002173767623182213650621663541964889984525, 196011684744279102200813294673265147565112904749903, 642418964718759637555214182527227480575132344578522
Generating function in Maple syntax:
-(5*x^3-8*x^2+5*x-1)/(3*x^4-11*x^3+12*x^2-6*x+1)
Generating function in latex syntax:
-\frac{5 x^{3}-8 x^{2}+5 x -1}{3 x^{4}-11 x^{3}+12 x^{2}-6 x +1}
Generating function in sympy syntax:
(-5*x**3 + 8*x**2 - 5*x + 1)/(3*x**4 - 11*x**3 + 12*x**2 - 6*x + 1)
Implicit equation for the generating function in Maple syntax:
(3*x^4-11*x^3+12*x^2-6*x+1)*F(x)+5*x^3-8*x^2+5*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(3 x^{4}-11 x^{3}+12 x^{2}-6 x +1\right) F \! \left(x \right)+5 x^{3}-8 x^{2}+5 x -1 = 0
Explicit closed form in Maple syntax:
9/41*Sum(_alpha^(-n+2),_alpha = RootOf(3*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1))-12/41*Sum(_alpha^(-n+1),_alpha = RootOf(3*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1))+8/41*Sum(_alpha^(-n),_alpha = RootOf(3*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1))+2/123*Sum(_alpha^(-n-1),_alpha = RootOf(3*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1))
Explicit closed form in latex syntax:
\frac{9 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(3 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +2}\right)}{41}-\frac{12 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(3 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +1}\right)}{41}+\frac{8 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(3 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{41}+\frac{2 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(3 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{123}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+4) = -3*a(n)+11*a(n+1)-12*a(n+2)+6*a(n+3), n >= 4
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(n +4\right) = -3 a \! \left(n \right)+11 a \! \left(n +1\right)-12 a \! \left(n +2\right)+6 a \! \left(n +3\right), \quad n \geq 4
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15931/
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[35,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[6,x]
F[10,x] = F[11,x]+F[23,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[14,x]+F[17,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]*F[4,x]
F[17,x] = F[11,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[22,x]
F[21,x] = F[15,x]
F[22,x] = F[18,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[27,x]+F[7,x]
F[27,x] = F[28,x]
F[28,x] = F[26,x]*F[4,x]
F[29,x] = F[23,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[27,x]
F[34,x] = F[30,x]
F[35,x] = F[36,x]+F[50,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[14,x]+F[39,x]
F[39,x] = F[36,x]+F[40,x]
F[40,x] = F[41,x]+F[42,x]+F[45,x]
F[41,x] = 0
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[21,x]+F[44,x]
F[44,x] = F[40,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[15,x]+F[47,x]
F[47,x] = F[41,x]+F[45,x]+F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[15,x]+F[47,x]
F[50,x] = F[41,x]+F[51,x]+F[63,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[26,x]+F[53,x]
F[53,x] = F[50,x]+F[54,x]
F[54,x] = 2*F[41,x]+F[55,x]+F[58,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[33,x]+F[57,x]
F[57,x] = F[54,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[60,x]+F[79,x]
F[60,x] = F[41,x]+F[61,x]+F[63,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[60,x]+F[7,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[65,x]+F[66,x]
F[65,x] = F[15,x]+F[60,x]
F[66,x] = F[67,x]+F[76,x]
F[67,x] = F[41,x]+F[48,x]+F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[46,x]+F[70,x]
F[70,x] = F[67,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]+F[75,x]
F[74,x] = F[47,x]
F[75,x] = F[71,x]
F[76,x] = 2*F[41,x]+F[77,x]+F[80,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[27,x]+F[79,x]
F[79,x] = 2*F[41,x]+F[58,x]+F[77,x]
F[80,x] = F[4,x]*F[81,x]
F[81,x] = F[59,x]+F[82,x]
F[82,x] = F[76,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[79,x]
F[87,x] = F[83,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_{35}\! \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_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{23}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{17}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \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_{21}\! \left(x \right)+F_{22}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{7}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{27}\! \left(x \right)
F_{34}\! \left(x \right) = F_{30}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{50}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{14}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{42}\! \left(x \right)+F_{45}\! \left(x \right)
F_{41}\! \left(x \right) = 0
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{21}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{40}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{15}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{41}\! \left(x \right)+F_{45}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{15}\! \left(x \right)+F_{47}\! \left(x \right)
F_{50}\! \left(x \right) = F_{41}\! \left(x \right)+F_{51}\! \left(x \right)+F_{63}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{26}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{50}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = 2 F_{41}\! \left(x \right)+F_{55}\! \left(x \right)+F_{58}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{33}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{54}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{79}\! \left(x \right)
F_{60}\! \left(x \right) = F_{41}\! \left(x \right)+F_{61}\! \left(x \right)+F_{63}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{60}\! \left(x \right)+F_{7}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{66}\! \left(x \right)
F_{65}\! \left(x \right) = F_{15}\! \left(x \right)+F_{60}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{76}\! \left(x \right)
F_{67}\! \left(x \right) = F_{41}\! \left(x \right)+F_{48}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{46}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{67}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{75}\! \left(x \right)
F_{74}\! \left(x \right) = F_{47}\! \left(x \right)
F_{75}\! \left(x \right) = F_{71}\! \left(x \right)
F_{76}\! \left(x \right) = 2 F_{41}\! \left(x \right)+F_{77}\! \left(x \right)+F_{80}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{27}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{41}\! \left(x \right)+F_{58}\! \left(x \right)+F_{77}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{59}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{76}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{79}\! \left(x \right)
F_{87}\! \left(x \right) = F_{83}\! \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_35(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_6(x))
Eq(F_10(x), F_11(x) + F_23(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_17(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)*F_4(x))
Eq(F_17(x), F_11(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_21(x) + F_22(x))
Eq(F_21(x), F_15(x))
Eq(F_22(x), F_18(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_27(x) + F_7(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_26(x)*F_4(x))
Eq(F_29(x), F_23(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_27(x))
Eq(F_34(x), F_30(x))
Eq(F_35(x), F_36(x) + F_50(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_14(x) + F_39(x))
Eq(F_39(x), F_36(x) + F_40(x))
Eq(F_40(x), F_41(x) + F_42(x) + F_45(x))
Eq(F_41(x), 0)
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_21(x) + F_44(x))
Eq(F_44(x), F_40(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_15(x) + F_47(x))
Eq(F_47(x), F_41(x) + F_45(x) + F_48(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_15(x) + F_47(x))
Eq(F_50(x), F_41(x) + F_51(x) + F_63(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_26(x) + F_53(x))
Eq(F_53(x), F_50(x) + F_54(x))
Eq(F_54(x), 2*F_41(x) + F_55(x) + F_58(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_33(x) + F_57(x))
Eq(F_57(x), F_54(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_79(x))
Eq(F_60(x), F_41(x) + F_61(x) + F_63(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_60(x) + F_7(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_66(x))
Eq(F_65(x), F_15(x) + F_60(x))
Eq(F_66(x), F_67(x) + F_76(x))
Eq(F_67(x), F_41(x) + F_48(x) + F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_46(x) + F_70(x))
Eq(F_70(x), F_67(x) + F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_75(x))
Eq(F_74(x), F_47(x))
Eq(F_75(x), F_71(x))
Eq(F_76(x), 2*F_41(x) + F_77(x) + F_80(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_27(x) + F_79(x))
Eq(F_79(x), 2*F_41(x) + F_58(x) + F_77(x))
Eq(F_80(x), F_4(x)*F_81(x))
Eq(F_81(x), F_59(x) + F_82(x))
Eq(F_82(x), F_76(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_79(x))
Eq(F_87(x), F_83(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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