0132_0231_1230_1320_3120
Counting sequence:
1, 1, 2, 6, 19, 58, 168, 463, 1223, 3120, 7738, 18757, 44625, 104542, 241772, 553083, 1253515, 2818204, 6291630, 13959361, 30802133, 67633386, 147849472, 321913111, 698351919, 1509949768, 3254780258, 6996099453, 14998831513, 32078037430, 68451041748, 145760453107, 309774516755, 657129996852, 1391569404502, 2942052598393, 6210522710685, 13091060318914, 27556510171880, 57930518889231, 121633473823543, 255086697644896, 534362651100042, 1118203325449141, 2337561720652769, 4881831627326478, 10185875719717948, 21233768555611243, 44226755715663003, 92042317384385740, 191402984163247358, 397724142092158257, 825847581669066085, 1713619658214475162, 3553340105995322832, 7363385390750762503, 15249188338276501055, 31561226188612437624, 65284180198362711730, 134963873633039025901, 278862888926781114153, 575884291551120066406, 1188662071249659234212, 2452264040298763519971, 5056713719205630838819, 10422410401645896665188, 21472010101797918083238, 44216845544681795225833, 91016235259682927675693, 187271345836299368008050, 385168016259055437744568, 791881829596203631774207, 1627445549158951481772615, 3343435469871708811299472, 6866320866092464140716762, 14096263951365890962885413, 28929217074059446579104625, 59350701956705701045734334, 121723718462447975028231180, 249567623886695010253409371, 511526737424439969547553963, 1048138685605883494470257916, 2147052255635581414278171982, 4396863205938406308406365601, 9001661652850528834862190069, 18424029490926948622522125898, 37699142758862596184037396128, 77119795884856424312856383223, 157721298130202980648866549583, 322483380233841561611221864360, 659203070919464996383783653378, 1347188247752315084158971940957, 2752559677351043041238202716345, 5622723658434197208591822229782, 11483131804411187429964276306292, 23446584344065102406589412807123, 47863713678929942948699739001395, 97688324380087928252839690769044, 199338056885889073385356579050230, 406678158185718844867661097079641, 829518861524347614604405160022973
Generating function in Maple syntax:
-(x^6+11*x^5-34*x^4+42*x^3-26*x^2+8*x-1)/(2*x-1)^3/(x-1)^3
Generating function in latex syntax:
-\frac{x^{6}+11 x^{5}-34 x^{4}+42 x^{3}-26 x^{2}+8 x -1}{\left(2 x -1\right)^{3} \left(x -1\right)^{3}}
Generating function in sympy syntax:
(-x**6 - 11*x**5 + 34*x**4 - 42*x**3 + 26*x**2 - 8*x + 1)/((x - 1)**3*(2*x - 1)**3)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^3*(x-1)^3*F(x)+x^6+11*x^5-34*x^4+42*x^3-26*x^2+8*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{3} \left(x -1\right)^{3} F \! \left(x \right)+x^{6}+11 x^{5}-34 x^{4}+42 x^{3}-26 x^{2}+8 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/16*(n^2+5*n-30)*2^n+1/2*n^2+1/2*n+3)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(n^{2}+5 n -30\right) 2^{n}}{16}+\frac{n^{2}}{2}+\frac{n}{2}+3 & \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) = 58
a(6) = 168
a(n+3) = 8*a(n)-12*a(n+1)+6*a(n+2)-1/2*(n-3)*(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) = 58
a \! \left(6\right) = 168
a \! \left(n +3\right) = 8 a \! \left(n \right)-12 a \! \left(n +1\right)+6 a \! \left(n +2\right)-\frac{\left(n -3\right) \left(n -2\right)}{2}, \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/19036/
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[33,x]
F[23,x] = F[24,x]
F[24,x] = F[12,x]*F[25,x]
F[25,x] = F[26,x]+F[27,x]
F[26,x] = F[1,x]+F[12,x]
F[27,x] = F[23,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[12,x]*F[30,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[12,x]
F[32,x] = F[28,x]
F[33,x] = F[18,x]+F[34,x]+F[76,x]
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[36,x]+F[52,x]
F[36,x] = F[37,x]+F[6,x]
F[37,x] = F[18,x]+F[38,x]+F[39,x]
F[38,x] = F[10,x]*F[12,x]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[12,x]+F[42,x]
F[42,x] = F[18,x]+F[38,x]+F[43,x]
F[43,x] = F[12,x]*F[41,x]
F[44,x] = F[45,x]+F[48,x]
F[45,x] = F[46,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[12,x]+F[45,x]
F[48,x] = 2*F[18,x]+F[49,x]+F[51,x]
F[49,x] = F[12,x]*F[50,x]
F[50,x] = F[42,x]+F[48,x]
F[51,x] = F[12,x]*F[44,x]
F[52,x] = F[33,x]+F[53,x]
F[53,x] = 2*F[18,x]+F[54,x]+F[58,x]
F[54,x] = F[12,x]*F[55,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[37,x]
F[57,x] = F[53,x]
F[58,x] = F[12,x]*F[59,x]
F[59,x] = F[60,x]+F[67,x]
F[60,x] = F[28,x]+F[61,x]
F[61,x] = 2*F[18,x]+F[62,x]+F[66,x]
F[62,x] = F[12,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[42,x]
F[65,x] = F[61,x]
F[66,x] = F[12,x]*F[60,x]
F[67,x] = F[68,x]+F[71,x]
F[68,x] = F[69,x]
F[69,x] = F[12,x]*F[70,x]
F[70,x] = F[28,x]+F[68,x]
F[71,x] = 2*F[18,x]+F[72,x]+F[73,x]+F[75,x]
F[72,x] = 0
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[61,x]+F[71,x]
F[75,x] = F[12,x]*F[67,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[78,x]+F[85,x]
F[78,x] = F[23,x]+F[79,x]
F[79,x] = F[18,x]+F[80,x]+F[84,x]
F[80,x] = F[12,x]*F[81,x]
F[81,x] = F[82,x]+F[83,x]
F[82,x] = F[10,x]+F[42,x]
F[83,x] = F[61,x]+F[79,x]
F[84,x] = F[12,x]*F[78,x]
F[85,x] = F[86,x]+F[89,x]
F[86,x] = F[18,x]+F[29,x]+F[87,x]
F[87,x] = F[12,x]*F[88,x]
F[88,x] = F[23,x]+F[86,x]
F[89,x] = F[18,x]+F[62,x]+F[90,x]+F[92,x]
F[90,x] = F[12,x]*F[91,x]
F[91,x] = F[79,x]+F[89,x]
F[92,x] = F[12,x]*F[85,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_{33}\! \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_{26}\! \left(x \right)+F_{27}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{27}\! \left(x \right) = F_{23}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right)
F_{32}\! \left(x \right) = F_{28}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18}\! \left(x \right)+F_{34}\! \left(x \right)+F_{76}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{52}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{6}\! \left(x \right)
F_{37}\! \left(x \right) = F_{18}\! \left(x \right)+F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{18}\! \left(x \right)+F_{38}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{48}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right)+F_{45}\! \left(x \right)
F_{48}\! \left(x \right) = 2 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_{42}\! \left(x \right)+F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{52}\! \left(x \right) = F_{33}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{54}\! \left(x \right)+F_{58}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{37}\! \left(x \right)
F_{57}\! \left(x \right) = F_{53}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{67}\! \left(x \right)
F_{60}\! \left(x \right) = F_{28}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{62}\! \left(x \right)+F_{66}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{42}\! \left(x \right)
F_{65}\! \left(x \right) = F_{61}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \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_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{28}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{72}\! \left(x \right)+F_{73}\! \left(x \right)+F_{75}\! \left(x \right)
F_{72}\! \left(x \right) = 0
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{61}\! \left(x \right)+F_{71}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{67}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{85}\! \left(x \right)
F_{78}\! \left(x \right) = F_{23}\! \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_{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_{10}\! \left(x \right)+F_{42}\! \left(x \right)
F_{83}\! \left(x \right) = F_{61}\! \left(x \right)+F_{79}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{89}\! \left(x \right)
F_{86}\! \left(x \right) = F_{18}\! \left(x \right)+F_{29}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{23}\! \left(x \right)+F_{86}\! \left(x \right)
F_{89}\! \left(x \right) = F_{18}\! \left(x \right)+F_{62}\! \left(x \right)+F_{90}\! \left(x \right)+F_{92}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{79}\! \left(x \right)+F_{89}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \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_33(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_12(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_27(x))
Eq(F_26(x), F_1(x) + F_12(x))
Eq(F_27(x), F_23(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_12(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_12(x))
Eq(F_32(x), F_28(x))
Eq(F_33(x), F_18(x) + F_34(x) + F_76(x))
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_52(x))
Eq(F_36(x), F_37(x) + F_6(x))
Eq(F_37(x), F_18(x) + F_38(x) + F_39(x))
Eq(F_38(x), F_10(x)*F_12(x))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_12(x) + F_42(x))
Eq(F_42(x), F_18(x) + F_38(x) + F_43(x))
Eq(F_43(x), F_12(x)*F_41(x))
Eq(F_44(x), F_45(x) + F_48(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_12(x) + F_45(x))
Eq(F_48(x), 2*F_18(x) + F_49(x) + F_51(x))
Eq(F_49(x), F_12(x)*F_50(x))
Eq(F_50(x), F_42(x) + F_48(x))
Eq(F_51(x), F_12(x)*F_44(x))
Eq(F_52(x), F_33(x) + F_53(x))
Eq(F_53(x), 2*F_18(x) + F_54(x) + F_58(x))
Eq(F_54(x), F_12(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_37(x))
Eq(F_57(x), F_53(x))
Eq(F_58(x), F_12(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_67(x))
Eq(F_60(x), F_28(x) + F_61(x))
Eq(F_61(x), 2*F_18(x) + F_62(x) + F_66(x))
Eq(F_62(x), F_12(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_42(x))
Eq(F_65(x), F_61(x))
Eq(F_66(x), F_12(x)*F_60(x))
Eq(F_67(x), F_68(x) + F_71(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_12(x)*F_70(x))
Eq(F_70(x), F_28(x) + F_68(x))
Eq(F_71(x), 2*F_18(x) + F_72(x) + F_73(x) + F_75(x))
Eq(F_72(x), 0)
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_61(x) + F_71(x))
Eq(F_75(x), F_12(x)*F_67(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_85(x))
Eq(F_78(x), F_23(x) + F_79(x))
Eq(F_79(x), F_18(x) + F_80(x) + F_84(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_10(x) + F_42(x))
Eq(F_83(x), F_61(x) + F_79(x))
Eq(F_84(x), F_12(x)*F_78(x))
Eq(F_85(x), F_86(x) + F_89(x))
Eq(F_86(x), F_18(x) + F_29(x) + F_87(x))
Eq(F_87(x), F_12(x)*F_88(x))
Eq(F_88(x), F_23(x) + F_86(x))
Eq(F_89(x), F_18(x) + F_62(x) + F_90(x) + F_92(x))
Eq(F_90(x), F_12(x)*F_91(x))
Eq(F_91(x), F_79(x) + F_89(x))
Eq(F_92(x), F_12(x)*F_85(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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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, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "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": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 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