0132_0213_1302_2301_3102
Counting sequence:
1, 1, 2, 6, 19, 53, 129, 282, 570, 1091, 2016, 3654, 6581, 11897, 21739, 40306, 75908, 145063, 280690, 548494, 1079735, 2136765, 4244101, 8450570, 16853598, 33647787, 67222068, 134354006, 268598409, 537064545, 1073970575, 2147752418, 4295281480, 8590300111, 17180292518, 34360226590, 68720037547, 137439595237, 274878638729, 549756645498, 1099512569794, 2199024319379, 4398047709000, 8796094367334, 17592187550877, 35184373771721, 70368746053107, 140737490440530, 281474979023948, 562949955982199, 1125899909671834, 2251799816804782, 4503599630803679, 9007199258512525, 18014398513617997, 36028797023492074, 72057594042877286, 144115188081257211, 288230376157597468, 576460752309827702, 1152921504613805553, 2305843009221244593, 4611686018435570199, 9223372036863631298, 18446744073719123856, 36893488147429437855, 73786976294849351246, 147573952589688417854, 295147905179365743187, 590295810358719536053, 1180591620717426211793, 2361183241434838598746, 4722366482869662351178, 9444732965739308775139, 18889465931478600480176, 37778931862957182682758, 75557863725914345813125, 151115727451828670728985, 302231454903657319142907, 604462909807314614477106, 1208925819614629203573012, 2417851639229258380110407, 4835703278458516731445698, 9671406556917033432288462, 19342813113834066832054535, 38685626227668133629572189, 77371252455336267222494485, 154742504910672534406123978, 309485009821345068771062126, 618970019642690137498508107, 1237940039285380274950856452, 2475880078570760549852892310, 4951760157141521099654181977, 9903520314283042199253853953, 19807040628566084398450161055, 39614081257132168796839604642, 79228162514264337593615183064, 158456325028528675187162888559, 316912650057057350374254701046, 633825300114114700748434575710, 1267650600228229401496790418171
Generating function in Maple syntax:
-(5*x^6-18*x^5+30*x^4-33*x^3+21*x^2-7*x+1)/(2*x-1)/(x-1)^6
Generating function in latex syntax:
-\frac{5 x^{6}-18 x^{5}+30 x^{4}-33 x^{3}+21 x^{2}-7 x +1}{\left(2 x -1\right) \left(x -1\right)^{6}}
Generating function in sympy syntax:
(-5*x**6 + 18*x**5 - 30*x**4 + 33*x**3 - 21*x**2 + 7*x - 1)/((x - 1)**6*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x-1)^6*F(x)+5*x^6-18*x^5+30*x^4-33*x^3+21*x^2-7*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x -1\right)^{6} F \! \left(x \right)+5 x^{6}-18 x^{5}+30 x^{4}-33 x^{3}+21 x^{2}-7 x +1 = 0
Explicit closed form in Maple syntax:
2^n-73/60*n+11/24*n^2-7/24*n^3+1/120*n^5+1/24*n^4
Explicit closed form in latex syntax:
2^{n}-\frac{73 n}{60}+\frac{11 n^{2}}{24}-\frac{7 n^{3}}{24}+\frac{n^{5}}{120}+\frac{n^{4}}{24}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 53
a(6) = 129
a(n+1) = 2*a(n)-1/120*(n-1)*(n^4+n^3-64*n^2+56*n-120), 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) = 53
a \! \left(6\right) = 129
a \! \left(n +1\right) = 2 a \! \left(n \right)-\frac{\left(n -1\right) \left(n^{4}+n^{3}-64 n^{2}+56 n -120\right)}{120}, \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18530/
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[21,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[7,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[1,x]+F[17,x]
F[20,x] = F[15,x]
F[21,x] = F[22,x]+F[38,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[6,x]
F[25,x] = F[22,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[16,x]+F[29,x]
F[29,x] = F[30,x]+F[31,x]
F[30,x] = F[27,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[37,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[17,x]+F[34,x]
F[37,x] = F[32,x]
F[38,x] = F[39,x]+F[40,x]+F[93,x]
F[39,x] = 0
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[54,x]
F[42,x] = F[43,x]+F[7,x]
F[43,x] = F[27,x]+F[39,x]+F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[49,x]
F[46,x] = F[11,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[46,x]
F[49,x] = F[14,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[20,x]+F[53,x]
F[53,x] = F[51,x]
F[54,x] = F[38,x]+F[55,x]
F[55,x] = 2*F[39,x]+F[56,x]+F[75,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[66,x]
F[58,x] = F[59,x]+F[64,x]
F[59,x] = F[39,x]+F[60,x]+F[62,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[11,x]+F[59,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[17,x]+F[59,x]
F[64,x] = F[65,x]
F[65,x] = F[4,x]*F[58,x]
F[66,x] = F[67,x]+F[71,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[34,x]+F[70,x]
F[70,x] = F[68,x]
F[71,x] = F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[70,x]+F[74,x]
F[74,x] = F[72,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[69,x]+F[77,x]
F[77,x] = F[78,x]+F[89,x]
F[78,x] = F[79,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[33,x]+F[81,x]
F[81,x] = F[78,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[85,x]+F[88,x]
F[85,x] = F[86,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[34,x]+F[85,x]
F[88,x] = F[83,x]
F[89,x] = F[90,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[85,x]+F[92,x]
F[92,x] = F[90,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[63,x]+F[95,x]
F[95,x] = F[30,x]+F[67,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_{21}\! \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_{7}\! \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_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{38}\! \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_{6}\! \left(x \right)
F_{25}\! \left(x \right) = F_{22}\! \left(x \right)+F_{26}\! \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_{16}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)
F_{30}\! \left(x \right) = F_{27}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{17}\! \left(x \right)+F_{34}\! \left(x \right)
F_{37}\! \left(x \right) = F_{32}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)+F_{93}\! \left(x \right)
F_{39}\! \left(x \right) = 0
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{54}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{7}\! \left(x \right)
F_{43}\! \left(x \right) = F_{27}\! \left(x \right)+F_{39}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{49}\! \left(x \right)
F_{46}\! \left(x \right) = F_{11}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{49}\! \left(x \right) = F_{14}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \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_{20}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{51}\! \left(x \right)
F_{54}\! \left(x \right) = F_{38}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = 2 F_{39}\! \left(x \right)+F_{56}\! \left(x \right)+F_{75}\! \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_{66}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{64}\! \left(x \right)
F_{59}\! \left(x \right) = F_{39}\! \left(x \right)+F_{60}\! \left(x \right)+F_{62}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{11}\! \left(x \right)+F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{17}\! \left(x \right)+F_{59}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{71}\! \left(x \right)
F_{67}\! \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_{34}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{68}\! \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_{70}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{69}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{89}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{33}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{78}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{88}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{34}\! \left(x \right)+F_{85}\! \left(x \right)
F_{88}\! \left(x \right) = F_{83}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{85}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{90}\! \left(x \right)
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{63}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{30}\! \left(x \right)+F_{67}\! \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_21(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_7(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_1(x) + F_17(x))
Eq(F_20(x), F_15(x))
Eq(F_21(x), F_22(x) + F_38(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_6(x))
Eq(F_25(x), F_22(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_16(x) + F_29(x))
Eq(F_29(x), F_30(x) + F_31(x))
Eq(F_30(x), F_27(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_37(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_17(x) + F_34(x))
Eq(F_37(x), F_32(x))
Eq(F_38(x), F_39(x) + F_40(x) + F_93(x))
Eq(F_39(x), 0)
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_54(x))
Eq(F_42(x), F_43(x) + F_7(x))
Eq(F_43(x), F_27(x) + F_39(x) + F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_49(x))
Eq(F_46(x), F_11(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_4(x)*F_46(x))
Eq(F_49(x), F_14(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_20(x) + F_53(x))
Eq(F_53(x), F_51(x))
Eq(F_54(x), F_38(x) + F_55(x))
Eq(F_55(x), 2*F_39(x) + F_56(x) + F_75(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_66(x))
Eq(F_58(x), F_59(x) + F_64(x))
Eq(F_59(x), F_39(x) + F_60(x) + F_62(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_11(x) + F_59(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_17(x) + F_59(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_4(x)*F_58(x))
Eq(F_66(x), F_67(x) + F_71(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_34(x) + F_70(x))
Eq(F_70(x), F_68(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_70(x) + F_74(x))
Eq(F_74(x), F_72(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_69(x) + F_77(x))
Eq(F_77(x), F_78(x) + F_89(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_33(x) + F_81(x))
Eq(F_81(x), F_78(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_88(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_34(x) + F_85(x))
Eq(F_88(x), F_83(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_85(x) + F_92(x))
Eq(F_92(x), F_90(x))
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_63(x) + F_95(x))
Eq(F_95(x), F_30(x) + F_67(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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