01324_01342_01432_03124_03142_03214_03241_03412_03421_04132_04312_04321_10324_10342_10432_13024_13042_13402_14032_14302_30124_30142_30214_30241_30412_30421_31024_31042_31402_34012_34021_34102_40132_40312_40321_41032_41302_43012_43021_43102
Counting sequence:
1, 1, 2, 6, 24, 80, 252, 770, 2304, 6786, 19740, 56848, 162360, 460486, 1298304, 3641790, 10169952, 28289360, 78419124, 216709706, 597214080, 1641703098, 4502702820, 12324057616, 33667619184, 91815595150, 249991402752, 679658527350, 1845271685544, 5003519133776, 13551086023020, 36659777252498, 99072560378880, 267480809500146, 721494270325164, 1944452302470160, 5236089137866152, 14089044312475990, 37882504902824064, 101787624504435246, 273316369832536560, 733440334550900048, 1967005181271285540, 5272298002058596826, 14124056655840303744, 37817652665474070570, 101208075609681377652, 270726316270856715280, 723850925255649257184, 1934546873547085870366, 5168070885485832307200, 13800788939160088096998, 36839384210643239167800, 98301505372466373912656, 262212468667197308904924, 699193769230753087300130, 1863795108069503130154752, 4966612493509452300143970, 13230878919009500584057404, 35236112964639293896389136, 93812889531718467624412440, 249698755599826124090394598, 664436547618879863468108160, 1767574198340863327664393886, 4701022810304739744755128704, 12499741210192394920940693840, 33228204990228532435856002452, 88310639292742425625654760810, 234651005314790326740401572224, 623358488399754078254402385306, 1655625502702056896700069579780, 4396405036411046054218745912848, 11672049613827384604397722839120, 30982236810255388331926147086766, 82223679825195318771794337187584, 218173366684915902551745996292950, 578801093280051854207897428375752, 1535259368287152721477018487070800, 4071560703926646029113920850861644, 10796144365396591461131960321352626, 28622453565629306921192846062686720, 75871238229686058907912019459340498, 201085745644646880052028651143743180, 532869430369713882391164808864481296, 1411878355939654660300952961299069064, 3740349637209270476907164757688238710, 9907566744493058012427466173882817152, 26239955162924586908000537667656210190, 69486716255439851512443133678056635664, 183985841570217730684310520009730166096, 487093334844522480904564409431812448260, 1289396094164454370066629000884526466298, 3412778214862845463042985487937546227840, 9031886420864991862268069854476630761226, 23900041391840854819630788355422122410644, 63236770916542836841027245660030546991120, 167298710499334723740790235689462173769152, 442556144844217274248958372154493129415230, 1170571637680037850571590325947636024566784, 3095867724873302592294714030463134219456966, 8186956493325368119233750594592305649229400
Generating function in Maple syntax:
(x-1)*(2*x^5-7*x^4-2*x^3-3*x^2+4*x-1)/(x^2-3*x+1)^2
Generating function in latex syntax:
\frac{\left(x -1\right) \left(2 x^{5}-7 x^{4}-2 x^{3}-3 x^{2}+4 x -1\right)}{\left(x^{2}-3 x +1\right)^{2}}
Generating function in sympy syntax:
(x - 1)*(2*x**5 - 7*x**4 - 2*x**3 - 3*x**2 + 4*x - 1)/(x**2 - 3*x + 1)**2
Implicit equation for the generating function in Maple syntax:
-(x^2-3*x+1)^2*F(x)+(x-1)*(2*x^5-7*x^4-2*x^3-3*x^2+4*x-1) = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{2}-3 x +1\right)^{2} F \! \left(x \right)+\left(x -1\right) \left(2 x^{5}-7 x^{4}-2 x^{3}-3 x^{2}+4 x -1\right) = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,3,n = 2,2,0)+1/5*(7*5^(1/2)*n-15*n)*(3/2-1/2*5^(1/2))^(-n)+1/5*(-7*5^(1/2)*n-15*n)*(3/2+1/2*5^(1/2))^(-n)
Explicit closed form in latex syntax:
\left(\left\{\begin{array}{cc}1 & n =0 \\ 3 & n =1 \\ 2 & n =2 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)+\frac{\left(7 \sqrt{5}\, n -15 n \right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{5}+\frac{\left(-7 \sqrt{5}\, n -15 n \right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{5}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 80
a(6) = 252
a(n+4) = -a(n)+6*a(n+1)-11*a(n+2)+6*a(n+3), n >= 7
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 80
a(6) = 252
a{\left(n + 4 \right)} = - a{\left(n \right)} + 6 a{\left(n + 1 \right)} - 11 a{\left(n + 2 \right)} + 6 a{\left(n + 3 \right)}, \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/25801/
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[36,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[18,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[10,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[1,x]+F[15,x]
F[18,x] = F[19,x]+F[27,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[17,x]+F[22,x]
F[22,x] = F[23,x]+F[4,x]
F[23,x] = F[24,x]+F[25,x]+F[26,x]
F[24,x] = 0
F[25,x] = F[15,x]*F[4,x]
F[26,x] = F[22,x]*F[4,x]
F[27,x] = F[24,x]+F[28,x]+F[30,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[11,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[35,x]
F[32,x] = F[33,x]+F[4,x]
F[33,x] = F[24,x]+F[30,x]+F[34,x]
F[34,x] = F[11,x]*F[4,x]
F[35,x] = F[23,x]
F[36,x] = F[37,x]+F[63,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[1,x]+F[19,x]
F[41,x] = F[42,x]+F[49,x]
F[42,x] = F[43,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[1,x]+F[4,x]
F[46,x] = F[42,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[42,x]
F[49,x] = F[24,x]+F[50,x]+F[61,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[15,x]+F[23,x]
F[53,x] = F[54,x]+F[57,x]
F[54,x] = F[24,x]+F[50,x]+F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[42,x]+F[54,x]
F[57,x] = 2*F[24,x]+F[58,x]+F[59,x]
F[58,x] = F[4,x]*F[54,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[47,x]+F[57,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[56,x]+F[60,x]
F[63,x] = F[24,x]+F[64,x]+F[87,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[11,x]+F[27,x]
F[67,x] = F[68,x]+F[83,x]
F[68,x] = F[24,x]+F[69,x]+F[79,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[11,x]+F[33,x]
F[72,x] = F[68,x]+F[73,x]
F[73,x] = 2*F[24,x]+F[74,x]+F[75,x]
F[74,x] = F[4,x]*F[68,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[47,x]+F[73,x]
F[78,x] = F[57,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[81,x]+F[82,x]
F[81,x] = F[42,x]+F[68,x]
F[82,x] = F[54,x]
F[83,x] = F[24,x]+F[75,x]+F[84,x]+F[85,x]
F[84,x] = 0
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[68,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[81,x]+F[89,x]
F[89,x] = F[49,x]+F[83,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_{36}\! \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_{18}\! \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_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{27}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{17}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{24}\! \left(x \right) = 0
F_{25}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{24}\! \left(x \right)+F_{28}\! \left(x \right)+F_{30}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{24}\! \left(x \right)+F_{30}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{23}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{63}\! \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_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{49}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{46}\! \left(x \right) = F_{42}\! \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_{42}\! \left(x \right)
F_{49}\! \left(x \right) = F_{24}\! \left(x \right)+F_{50}\! \left(x \right)+F_{61}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{15}\! \left(x \right)+F_{23}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{57}\! \left(x \right)
F_{54}\! \left(x \right) = F_{24}\! \left(x \right)+F_{50}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{42}\! \left(x \right)+F_{54}\! \left(x \right)
F_{57}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{47}\! \left(x \right)+F_{57}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{24}\! \left(x \right)+F_{64}\! \left(x \right)+F_{87}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{11}\! \left(x \right)+F_{27}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{83}\! \left(x \right)
F_{68}\! \left(x \right) = F_{24}\! \left(x \right)+F_{69}\! \left(x \right)+F_{79}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{11}\! \left(x \right)+F_{33}\! \left(x \right)
F_{72}\! \left(x \right) = F_{68}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{74}\! \left(x \right)+F_{75}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{47}\! \left(x \right)+F_{73}\! \left(x \right)
F_{78}\! \left(x \right) = F_{57}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{82}\! \left(x \right)
F_{81}\! \left(x \right) = F_{42}\! \left(x \right)+F_{68}\! \left(x \right)
F_{82}\! \left(x \right) = F_{54}\! \left(x \right)
F_{83}\! \left(x \right) = F_{24}\! \left(x \right)+F_{75}\! \left(x \right)+F_{84}\! \left(x \right)+F_{85}\! \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_{68}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{81}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{49}\! \left(x \right)+F_{83}\! \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_36(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_18(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_10(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_1(x) + F_15(x))
Eq(F_18(x), F_19(x) + F_27(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_17(x) + F_22(x))
Eq(F_22(x), F_23(x) + F_4(x))
Eq(F_23(x), F_24(x) + F_25(x) + F_26(x))
Eq(F_24(x), 0)
Eq(F_25(x), F_15(x)*F_4(x))
Eq(F_26(x), F_22(x)*F_4(x))
Eq(F_27(x), F_24(x) + F_28(x) + F_30(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_11(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_35(x))
Eq(F_32(x), F_33(x) + F_4(x))
Eq(F_33(x), F_24(x) + F_30(x) + F_34(x))
Eq(F_34(x), F_11(x)*F_4(x))
Eq(F_35(x), F_23(x))
Eq(F_36(x), F_37(x) + F_63(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_1(x) + F_19(x))
Eq(F_41(x), F_42(x) + F_49(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_1(x) + F_4(x))
Eq(F_46(x), F_42(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_4(x)*F_42(x))
Eq(F_49(x), F_24(x) + F_50(x) + F_61(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_15(x) + F_23(x))
Eq(F_53(x), F_54(x) + F_57(x))
Eq(F_54(x), F_24(x) + F_50(x) + F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_42(x) + F_54(x))
Eq(F_57(x), 2*F_24(x) + F_58(x) + F_59(x))
Eq(F_58(x), F_4(x)*F_54(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_47(x) + F_57(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_56(x) + F_60(x))
Eq(F_63(x), F_24(x) + F_64(x) + F_87(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_11(x) + F_27(x))
Eq(F_67(x), F_68(x) + F_83(x))
Eq(F_68(x), F_24(x) + F_69(x) + F_79(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_11(x) + F_33(x))
Eq(F_72(x), F_68(x) + F_73(x))
Eq(F_73(x), 2*F_24(x) + F_74(x) + F_75(x))
Eq(F_74(x), F_4(x)*F_68(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_47(x) + F_73(x))
Eq(F_78(x), F_57(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_82(x))
Eq(F_81(x), F_42(x) + F_68(x))
Eq(F_82(x), F_54(x))
Eq(F_83(x), F_24(x) + F_75(x) + F_84(x) + F_85(x))
Eq(F_84(x), 0)
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_68(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_81(x) + F_89(x))
Eq(F_89(x), F_49(x) + F_83(x))
Pack JSON:
{"name": "point_placements", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 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"pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 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[0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, {"class_module": 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