0123_0231_1032_2031_3201
Counting sequence:
1, 1, 2, 6, 19, 49, 98, 167, 255, 362, 488, 633, 797, 980, 1182, 1403, 1643, 1902, 2180, 2477, 2793, 3128, 3482, 3855, 4247, 4658, 5088, 5537, 6005, 6492, 6998, 7523, 8067, 8630, 9212, 9813, 10433, 11072, 11730, 12407, 13103, 13818, 14552, 15305, 16077, 16868, 17678, 18507, 19355, 20222, 21108, 22013, 22937, 23880, 24842, 25823, 26823, 27842, 28880, 29937, 31013, 32108, 33222, 34355, 35507, 36678, 37868, 39077, 40305, 41552, 42818, 44103, 45407, 46730, 48072, 49433, 50813, 52212, 53630, 55067, 56523, 57998, 59492, 61005, 62537, 64088, 65658, 67247, 68855, 70482, 72128, 73793, 75477, 77180, 78902, 80643, 82403, 84182, 85980, 87797, 89633
Generating function in Maple syntax:
(x^8-x^7-2*x^6-8*x^5-6*x^4-2*x^3-2*x^2+2*x-1)/(x-1)^3
Generating function in latex syntax:
\frac{x^{8}-x^{7}-2 x^{6}-8 x^{5}-6 x^{4}-2 x^{3}-2 x^{2}+2 x -1}{\left(x -1\right)^{3}}
Generating function in sympy syntax:
(x**8 - x**7 - 2*x**6 - 8*x**5 - 6*x**4 - 2*x**3 - 2*x**2 + 2*x - 1)/(x - 1)**3
Implicit equation for the generating function in Maple syntax:
-(x-1)^3*F(x)+x^8-x^7-2*x^6-8*x^5-6*x^4-2*x^3-2*x^2+2*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x -1\right)^{3} F \! \left(x \right)+x^{8}-x^{7}-2 x^{6}-8 x^{5}-6 x^{4}-2 x^{3}-2 x^{2}+2 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,n = 3,6,n = 4,19,n = 5,49,83-109/2*n+19/2*n^2)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ 6 & n =3 \\ 19 & n =4 \\ 49 & n =5 \\ 83-\frac{109}{2} n +\frac{19}{2} n^{2} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 49
a(6) = 98
a(7) = 167
a(8) = 255
a(n) = 83-109/2*n+19/2*n^2, n >= 9
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) = 98
a \! \left(7\right) = 167
a \! \left(8\right) = 255
a \! \left(n \right) = 83-\frac{109}{2} n +\frac{19}{2} n^{2}, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/17266/
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[27,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[22,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[10,x]+F[17,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[4,x]
F[21,x] = F[19,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[4,x]
F[26,x] = F[21,x]
F[27,x] = F[28,x]+F[59,x]
F[28,x] = F[29,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[1,x]+F[14,x]
F[32,x] = F[11,x]+F[33,x]
F[33,x] = F[34,x]+F[35,x]+F[47,x]
F[34,x] = 0
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[1,x]+F[4,x]
F[40,x] = F[34,x]+F[35,x]+F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[11,x]+F[43,x]
F[43,x] = F[34,x]+F[44,x]+F[46,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[4,x]+F[43,x]
F[46,x] = F[11,x]*F[4,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[49,x]+F[54,x]
F[49,x] = F[11,x]+F[50,x]
F[50,x] = F[34,x]+F[44,x]+F[51,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[11,x]+F[53,x]
F[53,x] = F[51,x]
F[54,x] = F[53,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[43,x]+F[58,x]
F[58,x] = F[56,x]
F[59,x] = F[34,x]+F[60,x]+F[78,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[62,x]+F[64,x]
F[62,x] = F[37,x]+F[63,x]
F[63,x] = F[23,x]
F[64,x] = F[40,x]+F[65,x]
F[65,x] = 2*F[34,x]+F[66,x]+F[74,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[71,x]
F[68,x] = F[69,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[4,x]
F[71,x] = 2*F[34,x]+F[66,x]+F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[43,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[43,x]
F[77,x] = F[58,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[95,x]
F[80,x] = F[28,x]+F[81,x]
F[81,x] = F[34,x]+F[82,x]+F[92,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[84,x]+F[86,x]
F[84,x] = F[4,x]+F[85,x]
F[85,x] = F[23,x]
F[86,x] = F[43,x]+F[87,x]
F[87,x] = 2*F[34,x]+F[74,x]+F[88,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[69,x]
F[91,x] = 2*F[34,x]+F[72,x]+F[88,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[28,x]+F[94,x]
F[94,x] = F[34,x]+F[51,x]+F[82,x]
F[95,x] = F[96,x]+F[97,x]
F[96,x] = F[34,x]+F[47,x]+F[60,x]
F[97,x] = 2*F[34,x]+F[74,x]+F[98,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[90,x]
F[101,x] = F[91,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_{27}\! \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_{22}\! \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_{10}\! \left(x \right)+F_{17}\! \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_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{21}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{59}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{32}\! \left(x \right) = F_{11}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)+F_{47}\! \left(x \right)
F_{34}\! \left(x \right) = 0
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \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_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{40}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \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_{34}\! \left(x \right)+F_{44}\! \left(x \right)+F_{46}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right)+F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{54}\! \left(x \right)
F_{49}\! \left(x \right) = F_{11}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{34}\! \left(x \right)+F_{44}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{11}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{51}\! \left(x \right)
F_{54}\! \left(x \right) = F_{53}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{43}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{56}\! \left(x \right)
F_{59}\! \left(x \right) = F_{34}\! \left(x \right)+F_{60}\! \left(x \right)+F_{78}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{64}\! \left(x \right)
F_{62}\! \left(x \right) = F_{37}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{23}\! \left(x \right)
F_{64}\! \left(x \right) = F_{40}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{66}\! \left(x \right)+F_{74}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{71}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{66}\! \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_{43}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \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_{43}\! \left(x \right)
F_{77}\! \left(x \right) = F_{58}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{95}\! \left(x \right)
F_{80}\! \left(x \right) = F_{28}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{34}\! \left(x \right)+F_{82}\! \left(x \right)+F_{92}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{86}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{23}\! \left(x \right)
F_{86}\! \left(x \right) = F_{43}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{74}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{69}\! \left(x \right)
F_{91}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{72}\! \left(x \right)+F_{88}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{28}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{34}\! \left(x \right)+F_{51}\! \left(x \right)+F_{82}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{97}\! \left(x \right)
F_{96}\! \left(x \right) = F_{34}\! \left(x \right)+F_{47}\! \left(x \right)+F_{60}\! \left(x \right)
F_{97}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{74}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{90}\! \left(x \right)
F_{101}\! \left(x \right) = F_{91}\! \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_27(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_22(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_10(x) + F_17(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_4(x))
Eq(F_21(x), F_19(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_4(x))
Eq(F_26(x), F_21(x))
Eq(F_27(x), F_28(x) + F_59(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_1(x) + F_14(x))
Eq(F_32(x), F_11(x) + F_33(x))
Eq(F_33(x), F_34(x) + F_35(x) + F_47(x))
Eq(F_34(x), 0)
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_1(x) + F_4(x))
Eq(F_40(x), F_34(x) + F_35(x) + F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_11(x) + F_43(x))
Eq(F_43(x), F_34(x) + F_44(x) + F_46(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_4(x) + F_43(x))
Eq(F_46(x), F_11(x)*F_4(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_54(x))
Eq(F_49(x), F_11(x) + F_50(x))
Eq(F_50(x), F_34(x) + F_44(x) + F_51(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_11(x) + F_53(x))
Eq(F_53(x), F_51(x))
Eq(F_54(x), F_53(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_43(x) + F_58(x))
Eq(F_58(x), F_56(x))
Eq(F_59(x), F_34(x) + F_60(x) + F_78(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_64(x))
Eq(F_62(x), F_37(x) + F_63(x))
Eq(F_63(x), F_23(x))
Eq(F_64(x), F_40(x) + F_65(x))
Eq(F_65(x), 2*F_34(x) + F_66(x) + F_74(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_71(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_4(x))
Eq(F_71(x), 2*F_34(x) + F_66(x) + F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_43(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_43(x))
Eq(F_77(x), F_58(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_95(x))
Eq(F_80(x), F_28(x) + F_81(x))
Eq(F_81(x), F_34(x) + F_82(x) + F_92(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_86(x))
Eq(F_84(x), F_4(x) + F_85(x))
Eq(F_85(x), F_23(x))
Eq(F_86(x), F_43(x) + F_87(x))
Eq(F_87(x), 2*F_34(x) + F_74(x) + F_88(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_69(x))
Eq(F_91(x), 2*F_34(x) + F_72(x) + F_88(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_28(x) + F_94(x))
Eq(F_94(x), F_34(x) + F_51(x) + F_82(x))
Eq(F_95(x), F_96(x) + F_97(x))
Eq(F_96(x), F_34(x) + F_47(x) + F_60(x))
Eq(F_97(x), 2*F_34(x) + F_74(x) + F_98(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_90(x))
Eq(F_101(x), F_91(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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1], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 1], "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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