0132_0231_1032_3021_3120
Counting sequence:
1, 1, 2, 6, 19, 56, 154, 400, 994, 2388, 5590, 12824, 28954, 64540, 142366, 311328, 675874, 1458212, 3129382, 6684712, 14221354, 30146604, 63701038, 134217776, 282066994, 591396916, 1237319734, 2583691320, 5385486394, 11207180348, 23286775870, 48318382144, 100126425154, 207232172100, 428422987846, 884763263048, 1825361100874, 3762391351372, 7748121002062, 15942918602832, 32779190403154, 67345087201364, 138263587192918, 283673999966296, 581641651093594, 1191870604509276, 2440915813662814, 4996180836614240, 10221060091805794, 20899517020766308, 42713827715842150, 87257242780303464, 178173660257845354, 363665669910167660, 741968038609289326, 1513209474796486768, 3084965744748789874, 6287025079809212532, 12808237340241690742, 26084849041729912952, 53106446805952888954, 108086391056891904124, 219919777003756060798, 447333543787456626816, 909655067134802264194, 1849286093389382549636, 3758524105018321141894, 7636952046515754369160, 15513711765989732909194, 31507038877895914160268, 63973308447624725004430, 129865078278915243376784, 263567079325162073489554, 534808004184987320451220, 1084963699439300987846806, 2200622781017254669582488, 4462636326311814726942874, 9048054181178240229441692, 18341671419465702009995422, 37174468953149847122215072, 75331190134736580448878754, 152626884726346933306654884, 309182778366441411431104678, 626223574560377912497799336, 1268163184775746004266778794, 2567758440861472367075917996, 5198381024342905451236556974, 10522490333925732336642556080, 21296437238331307541623996594, 43095787617622300819925762228, 87197401517163973113207062710, 176406455598166689173125202104, 356836216324010864239672557754, 721719042903376700266189422780, 1459531306317463344106067460286, 2951249053656346575359512150208, 5966870989355532925013778759874, 12062487742796745398617066438852, 24382467013764849894413150716102, 49279917083872417983184337109192, 99589800280430272355084745572554
Generating function in Maple syntax:
(x^6+x^4-5*x^3+9*x^2-5*x+1)/(2*x-1)^2/(-1+x)^2
Generating function in latex syntax:
\frac{x^{6}+x^{4}-5 x^{3}+9 x^{2}-5 x +1}{\left(2 x -1\right)^{2} \left(-1+x \right)^{2}}
Generating function in sympy syntax:
(x**6 + x**4 - 5*x**3 + 9*x**2 - 5*x + 1)/((x - 1)**2*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
-(2*x-1)^2*(-1+x)^2*F(x)+x^6+x^4-5*x^3+9*x^2-5*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right)^{2} \left(-1+x \right)^{2} F \! \left(x \right)+x^{6}+x^{4}-5 x^{3}+9 x^{2}-5 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,1/16*(13*n-43)*2^n+2*n+2)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ \frac{\left(13 n -43\right) 2^{n}}{16}+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) = 56
a(6) = 154
a(n+2) = -4*a(n)+4*a(n+1)+2*n-2, n >= 7
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) = 56
a \! \left(6\right) = 154
a \! \left(n +2\right) = -4 a \! \left(n \right)+4 a \! \left(n +1\right)+2 n -2, \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/21710/
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[16,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[16,x]*F[7,x]
F[7,x] = F[8,x]+F[87,x]
F[8,x] = F[46,x]+F[9,x]
F[9,x] = F[10,x]+F[26,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]*F[16,x]
F[12,x] = F[13,x]+F[17,x]
F[13,x] = F[1,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[16,x]
F[16,x] = x
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[19,x]
F[19,x] = F[16,x]*F[20,x]
F[20,x] = F[1,x]+F[19,x]
F[21,x] = F[22,x]+F[23,x]+F[25,x]
F[22,x] = 0
F[23,x] = F[16,x]*F[24,x]
F[24,x] = F[14,x]+F[21,x]
F[25,x] = F[16,x]*F[17,x]
F[26,x] = F[16,x]+F[27,x]
F[27,x] = F[22,x]+F[28,x]+F[30,x]
F[28,x] = F[16,x]*F[29,x]
F[29,x] = F[11,x]
F[30,x] = F[16,x]*F[31,x]
F[31,x] = F[32,x]+F[36,x]
F[32,x] = F[16,x]+F[33,x]
F[33,x] = F[22,x]+F[34,x]+F[35,x]
F[34,x] = F[14,x]*F[16,x]
F[35,x] = F[16,x]*F[32,x]
F[36,x] = F[37,x]+F[41,x]
F[37,x] = F[22,x]+F[38,x]+F[39,x]
F[38,x] = F[16,x]*F[18,x]
F[39,x] = F[16,x]*F[40,x]
F[40,x] = F[16,x]+F[37,x]
F[41,x] = F[22,x]+F[42,x]+F[43,x]+F[45,x]
F[42,x] = F[16,x]*F[21,x]
F[43,x] = F[16,x]*F[44,x]
F[44,x] = F[33,x]+F[41,x]
F[45,x] = F[16,x]*F[36,x]
F[46,x] = F[47,x]*F[74,x]
F[47,x] = F[48,x]
F[48,x] = F[16,x]*F[49,x]
F[49,x] = F[50,x]+F[58,x]
F[50,x] = F[1,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[16,x]*F[53,x]
F[53,x] = F[13,x]+F[54,x]
F[54,x] = F[18,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[16,x]*F[57,x]
F[57,x] = F[14,x]+F[55,x]
F[58,x] = F[18,x]+F[59,x]
F[59,x] = F[22,x]+F[60,x]+F[65,x]
F[60,x] = F[16,x]*F[61,x]
F[61,x] = F[14,x]+F[62,x]
F[62,x] = F[22,x]+F[60,x]+F[63,x]
F[63,x] = F[16,x]*F[64,x]
F[64,x] = F[18,x]+F[62,x]
F[65,x] = F[16,x]*F[66,x]
F[66,x] = F[64,x]+F[67,x]
F[67,x] = F[68,x]+F[71,x]
F[68,x] = F[69,x]
F[69,x] = F[16,x]*F[70,x]
F[70,x] = F[18,x]+F[68,x]
F[71,x] = F[72,x]
F[72,x] = F[16,x]*F[73,x]
F[73,x] = F[62,x]+F[71,x]
F[74,x] = F[10,x]+F[75,x]
F[75,x] = F[16,x]+F[76,x]
F[76,x] = F[22,x]+F[34,x]+F[77,x]
F[77,x] = F[16,x]*F[78,x]
F[78,x] = F[32,x]+F[79,x]
F[79,x] = F[80,x]+F[83,x]
F[80,x] = F[81,x]
F[81,x] = F[16,x]*F[82,x]
F[82,x] = F[16,x]+F[80,x]
F[83,x] = 2*F[22,x]+F[84,x]+F[86,x]
F[84,x] = F[16,x]*F[85,x]
F[85,x] = F[33,x]+F[83,x]
F[86,x] = F[16,x]*F[79,x]
F[87,x] = F[88,x]+F[95,x]
F[88,x] = F[10,x]*F[89,x]
F[89,x] = F[90,x]+F[92,x]
F[90,x] = F[18,x]*F[91,x]
F[91,x] = F[1,x]+F[16,x]
F[92,x] = F[93,x]
F[93,x] = F[16,x]*F[94,x]
F[94,x] = F[51,x]+F[59,x]
F[95,x] = F[18,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_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{16}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)+F_{87}\! \left(x \right)
F_{8}\! \left(x \right) = F_{46}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{26}\! \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_{16}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{17}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{16}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{16}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{14}\! \left(x \right)+F_{21}\! \left(x \right)
F_{25}\! \left(x \right) = F_{16}\! \left(x \right) F_{17}\! \left(x \right)
F_{26}\! \left(x \right) = F_{16}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{22}\! \left(x \right)+F_{28}\! \left(x \right)+F_{30}\! \left(x \right)
F_{28}\! \left(x \right) = F_{16}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)
F_{30}\! \left(x \right) = F_{16}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{32}\! \left(x \right) = F_{16}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{22}\! \left(x \right)+F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right)
F_{35}\! \left(x \right) = F_{16}\! \left(x \right) F_{32}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{37}\! \left(x \right) = F_{22}\! \left(x \right)+F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{16}\! \left(x \right) F_{18}\! \left(x \right)
F_{39}\! \left(x \right) = F_{16}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \left(x \right)+F_{37}\! \left(x \right)
F_{41}\! \left(x \right) = F_{22}\! \left(x \right)+F_{42}\! \left(x \right)+F_{43}\! \left(x \right)+F_{45}\! \left(x \right)
F_{42}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right)
F_{43}\! \left(x \right) = F_{16}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{33}\! \left(x \right)+F_{41}\! \left(x \right)
F_{45}\! \left(x \right) = F_{16}\! \left(x \right) F_{36}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right) F_{74}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{16}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{58}\! \left(x \right)
F_{50}\! \left(x \right) = F_{1}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{16}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{13}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{18}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{16}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{14}\! \left(x \right)+F_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{18}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{22}\! \left(x \right)+F_{60}\! \left(x \right)+F_{65}\! \left(x \right)
F_{60}\! \left(x \right) = F_{16}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{14}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{22}\! \left(x \right)+F_{60}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{16}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{18}\! \left(x \right)+F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{16}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{64}\! \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_{16}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{18}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{16}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{62}\! \left(x \right)+F_{71}\! \left(x \right)
F_{74}\! \left(x \right) = F_{10}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{16}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{22}\! \left(x \right)+F_{34}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{16}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{32}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{83}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{16}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{16}\! \left(x \right)+F_{80}\! \left(x \right)
F_{83}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{84}\! \left(x \right)+F_{86}\! \left(x \right)
F_{84}\! \left(x \right) = F_{16}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{33}\! \left(x \right)+F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{16}\! \left(x \right) F_{79}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{95}\! \left(x \right)
F_{88}\! \left(x \right) = F_{10}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{92}\! \left(x \right)
F_{90}\! \left(x \right) = F_{18}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{16}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{51}\! \left(x \right)+F_{59}\! \left(x \right)
F_{95}\! \left(x \right) = F_{18}\! \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_16(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_16(x)*F_7(x))
Eq(F_7(x), F_8(x) + F_87(x))
Eq(F_8(x), F_46(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_26(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x)*F_16(x))
Eq(F_12(x), F_13(x) + F_17(x))
Eq(F_13(x), F_1(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_16(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_16(x)*F_20(x))
Eq(F_20(x), F_1(x) + F_19(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_25(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_16(x)*F_24(x))
Eq(F_24(x), F_14(x) + F_21(x))
Eq(F_25(x), F_16(x)*F_17(x))
Eq(F_26(x), F_16(x) + F_27(x))
Eq(F_27(x), F_22(x) + F_28(x) + F_30(x))
Eq(F_28(x), F_16(x)*F_29(x))
Eq(F_29(x), F_11(x))
Eq(F_30(x), F_16(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_36(x))
Eq(F_32(x), F_16(x) + F_33(x))
Eq(F_33(x), F_22(x) + F_34(x) + F_35(x))
Eq(F_34(x), F_14(x)*F_16(x))
Eq(F_35(x), F_16(x)*F_32(x))
Eq(F_36(x), F_37(x) + F_41(x))
Eq(F_37(x), F_22(x) + F_38(x) + F_39(x))
Eq(F_38(x), F_16(x)*F_18(x))
Eq(F_39(x), F_16(x)*F_40(x))
Eq(F_40(x), F_16(x) + F_37(x))
Eq(F_41(x), F_22(x) + F_42(x) + F_43(x) + F_45(x))
Eq(F_42(x), F_16(x)*F_21(x))
Eq(F_43(x), F_16(x)*F_44(x))
Eq(F_44(x), F_33(x) + F_41(x))
Eq(F_45(x), F_16(x)*F_36(x))
Eq(F_46(x), F_47(x)*F_74(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_16(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_58(x))
Eq(F_50(x), F_1(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_16(x)*F_53(x))
Eq(F_53(x), F_13(x) + F_54(x))
Eq(F_54(x), F_18(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_16(x)*F_57(x))
Eq(F_57(x), F_14(x) + F_55(x))
Eq(F_58(x), F_18(x) + F_59(x))
Eq(F_59(x), F_22(x) + F_60(x) + F_65(x))
Eq(F_60(x), F_16(x)*F_61(x))
Eq(F_61(x), F_14(x) + F_62(x))
Eq(F_62(x), F_22(x) + F_60(x) + F_63(x))
Eq(F_63(x), F_16(x)*F_64(x))
Eq(F_64(x), F_18(x) + F_62(x))
Eq(F_65(x), F_16(x)*F_66(x))
Eq(F_66(x), F_64(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_16(x)*F_70(x))
Eq(F_70(x), F_18(x) + F_68(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_16(x)*F_73(x))
Eq(F_73(x), F_62(x) + F_71(x))
Eq(F_74(x), F_10(x) + F_75(x))
Eq(F_75(x), F_16(x) + F_76(x))
Eq(F_76(x), F_22(x) + F_34(x) + F_77(x))
Eq(F_77(x), F_16(x)*F_78(x))
Eq(F_78(x), F_32(x) + F_79(x))
Eq(F_79(x), F_80(x) + F_83(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_16(x)*F_82(x))
Eq(F_82(x), F_16(x) + F_80(x))
Eq(F_83(x), 2*F_22(x) + F_84(x) + F_86(x))
Eq(F_84(x), F_16(x)*F_85(x))
Eq(F_85(x), F_33(x) + F_83(x))
Eq(F_86(x), F_16(x)*F_79(x))
Eq(F_87(x), F_88(x) + F_95(x))
Eq(F_88(x), F_10(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_92(x))
Eq(F_90(x), F_18(x)*F_91(x))
Eq(F_91(x), F_1(x) + F_16(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_16(x)*F_94(x))
Eq(F_94(x), F_51(x) + F_59(x))
Eq(F_95(x), F_18(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": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "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, 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": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "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, 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": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "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, 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": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "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": false, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 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[[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 0], [0, 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