0132_0321_1203_1230_3012
Counting sequence:
1, 1, 2, 6, 19, 49, 114, 270, 661, 1664, 4266, 11051, 28784, 75176, 196595, 514434, 1346504, 3524845, 9227766, 24158154, 63246361, 165580556, 433494894, 1134903671, 2971215620, 7778742644, 20365011719, 53316291870, 139583863196, 365435296969, 956722026906, 2504730782886, 6557470320829, 17167680178616, 44945570213970, 117669030462179, 308061521171384, 806515533050720, 2111485077979451, 5527939700886234, 14472334024677776, 37889062373145541, 99194853094757214, 259695496911124386, 679891637638614145, 1779979416004716164, 4660046610375532374, 12200160415121878895, 31940434634990102156, 83621143489848425324, 218922995834555171471, 573147844013817086646, 1500520536206896085924, 3928413764606871168481, 10284720757613717416770, 26925748508234281078974, 70492524767089125817189, 184551825793033096369520, 483162952612010163288186, 1264937032042997393491739, 3311648143516982017183616, 8670007398507948658055576, 22698374052006863956979459, 59425114757512643212879026, 155576970220531065681653720, 407305795904080553832078109, 1066340417491710595814576454, 2791715456571051233611646970, 7308805952221443105020360041, 19134702400093278081449428604, 50095301248058391139327921086, 131151201344081895336534329831, 343358302784187294870275063444, 898923707008479989274290855396, 2353412818241252672952597497495, 6161314747715278029583501631694, 16130531424904581415797907392044, 42230279526998466217810220538745, 110560307156090817237632754218346, 289450641941273985495088042110294, 757791618667731139247631372106381, 1983924214061919432247806074202536, 5193981023518027157495786850494754, 13598018856492162040239554477275091, 35600075545958458963222876581323720, 93202207781383214849429075266689104, 244006547798191185585064349218736459, 638817435613190341905763972389512970, 1672445759041379840132227567949794976, 4378519841510949178490918731459864309, 11463113765491467695340528626429790126, 30010821454963453907530667147829498066, 78569350599398894027251472817058695889, 205697230343233228174223751303346581236, 538522340430300790495419781092981039270, 1409869790947669143312035591975596527839, 3691087032412706639440686994833808535324, 9663391306290450775010025392525829069020, 25299086886458645685589389182743678662431, 66233869353085486281758142155705206908774, 173402521172797813159685037284371942054196
Generating function in Maple syntax:
-(x^9-6*x^8+10*x^7-8*x^5+2*x^4-6*x^3+9*x^2-5*x+1)/(x^2-3*x+1)/(x-1)^3
Generating function in latex syntax:
-\frac{x^{9}-6 x^{8}+10 x^{7}-8 x^{5}+2 x^{4}-6 x^{3}+9 x^{2}-5 x +1}{\left(x^{2}-3 x +1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(-x**9 + 6*x**8 - 10*x**7 + 8*x**5 - 2*x**4 + 6*x**3 - 9*x**2 + 5*x - 1)/((x - 1)**3*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
(x^2-3*x+1)*(x-1)^3*F(x)+x^9-6*x^8+10*x^7-8*x^5+2*x^4-6*x^3+9*x^2-5*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}-3 x +1\right) \left(x -1\right)^{3} F \! \left(x \right)+x^{9}-6 x^{8}+10 x^{7}-8 x^{5}+2 x^{4}-6 x^{3}+9 x^{2}-5 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),5,n = 2,3,n = 4,-1,0)+1/10*(5-5^(1/2))*(3/2-1/2*5^(1/2))^(-n)+1/10*(5+5^(1/2))*(3/2+1/2*5^(1/2))^(-n)+n^2-n-5
Explicit closed form in latex syntax:
\left(\left\{\begin{array}{cc}5 & n =0\text{ or } n =1 \\ 3 & n =2 \\ -1 & n =4 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)+\frac{\left(5-\sqrt{5}\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{10}+\frac{\left(5+\sqrt{5}\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{10}+n^{2}-n -5
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 49
a(6) = 114
a(7) = 270
a(8) = 661
a(9) = 1664
a(n+2) = -n^2+3*a(n+1)-a(n)-n+7, n >= 10
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) = 49
a \! \left(6\right) = 114
a \! \left(7\right) = 270
a \! \left(8\right) = 661
a \! \left(9\right) = 1664
a \! \left(n +2\right) = -n^{2}+3 a \! \left(n +1\right)-a \! \left(n \right)-n +7, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/19399/
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[25,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[17,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[1,x]+F[4,x]
F[17,x] = F[18,x]+F[19,x]+F[23,x]
F[18,x] = 0
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[11,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[11,x]*F[4,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[14,x]
F[25,x] = F[26,x]+F[64,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[1,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[16,x]*F[4,x]
F[32,x] = F[26,x]+F[33,x]
F[33,x] = F[18,x]+F[34,x]+F[62,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[36,x]+F[40,x]
F[36,x] = F[30,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[4,x]
F[40,x] = F[33,x]+F[41,x]
F[41,x] = 2*F[18,x]+F[42,x]+F[46,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = F[37,x]
F[45,x] = F[41,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[18,x]+F[49,x]+F[61,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[54,x]
F[51,x] = F[4,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = x^2
F[54,x] = F[48,x]+F[55,x]
F[55,x] = 2*F[18,x]+F[56,x]+F[60,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[52,x]
F[59,x] = F[55,x]
F[60,x] = F[4,x]*F[48,x]
F[61,x] = F[26,x]*F[4,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[26,x]+F[48,x]
F[64,x] = F[18,x]+F[65,x]+F[87,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]+F[78,x]
F[67,x] = F[68,x]+F[7,x]
F[68,x] = F[18,x]+F[69,x]+F[74,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[11,x]+F[71,x]
F[71,x] = F[18,x]+F[22,x]+F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[4,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[73,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = x^2
F[78,x] = F[64,x]+F[79,x]
F[79,x] = F[18,x]+F[80,x]+F[84,x]+F[85,x]
F[80,x] = F[4,x]*F[81,x]
F[81,x] = F[82,x]+F[83,x]
F[82,x] = F[68,x]
F[83,x] = F[79,x]
F[84,x] = 0
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[48,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[89,x]+F[90,x]
F[89,x] = F[26,x]
F[90,x] = F[91,x]
F[91,x] = F[18,x]+F[49,x]+F[92,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[26,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_{25}\! \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_{17}\! \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_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{23}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{11}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{14}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{64}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{26}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18}\! \left(x \right)+F_{34}\! \left(x \right)+F_{62}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right)
F_{40}\! \left(x \right) = F_{33}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{42}\! \left(x \right)+F_{46}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{37}\! \left(x \right)
F_{45}\! \left(x \right) = F_{41}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{18}\! \left(x \right)+F_{49}\! \left(x \right)+F_{61}\! \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_{54}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = x^{2}
F_{54}\! \left(x \right) = F_{48}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{52}\! \left(x \right)
F_{59}\! \left(x \right) = F_{55}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{61}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{26}\! \left(x \right)+F_{48}\! \left(x \right)
F_{64}\! \left(x \right) = F_{18}\! \left(x \right)+F_{65}\! \left(x \right)+F_{87}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{78}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{7}\! \left(x \right)
F_{68}\! \left(x \right) = F_{18}\! \left(x \right)+F_{69}\! \left(x \right)+F_{74}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{11}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \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_{4}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{73}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = x^{2}
F_{78}\! \left(x \right) = F_{64}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{18}\! \left(x \right)+F_{80}\! \left(x \right)+F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \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_{68}\! \left(x \right)
F_{83}\! \left(x \right) = F_{79}\! \left(x \right)
F_{84}\! \left(x \right) = 0
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{48}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{26}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{18}\! \left(x \right)+F_{49}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{26}\! \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_25(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_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_1(x) + F_4(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_23(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_11(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_11(x)*F_4(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_14(x))
Eq(F_25(x), F_26(x) + F_64(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_1(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_16(x)*F_4(x))
Eq(F_32(x), F_26(x) + F_33(x))
Eq(F_33(x), F_18(x) + F_34(x) + F_62(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_40(x))
Eq(F_36(x), F_30(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_4(x))
Eq(F_40(x), F_33(x) + F_41(x))
Eq(F_41(x), 2*F_18(x) + F_42(x) + F_46(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), F_37(x))
Eq(F_45(x), F_41(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_18(x) + F_49(x) + F_61(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_54(x))
Eq(F_51(x), F_4(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), x**2)
Eq(F_54(x), F_48(x) + F_55(x))
Eq(F_55(x), 2*F_18(x) + F_56(x) + F_60(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_52(x))
Eq(F_59(x), F_55(x))
Eq(F_60(x), F_4(x)*F_48(x))
Eq(F_61(x), F_26(x)*F_4(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_26(x) + F_48(x))
Eq(F_64(x), F_18(x) + F_65(x) + F_87(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_78(x))
Eq(F_67(x), F_68(x) + F_7(x))
Eq(F_68(x), F_18(x) + F_69(x) + F_74(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_11(x) + F_71(x))
Eq(F_71(x), F_18(x) + F_22(x) + F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_4(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_73(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), x**2)
Eq(F_78(x), F_64(x) + F_79(x))
Eq(F_79(x), F_18(x) + F_80(x) + F_84(x) + F_85(x))
Eq(F_80(x), F_4(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_83(x))
Eq(F_82(x), F_68(x))
Eq(F_83(x), F_79(x))
Eq(F_84(x), 0)
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_48(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_90(x))
Eq(F_89(x), F_26(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_18(x) + F_49(x) + F_92(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_26(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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": 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