01234_01243_01324_02134_02143_02314_03124_03214_12304_13204
Counting sequence:
1, 1, 2, 6, 24, 110, 544, 2833, 15346, 85722, 490606, 2863087, 16976590, 102002124, 619728370, 3801065092, 23503840994, 146361351590, 917012985914, 5776423798858, 36559673984880, 232365972436137, 1482419399486666, 9489151399090884, 60924772820660984, 392231562934983379, 2531402783448972158, 16373886209441822678, 106127375636252667062, 689146439079634656745, 4482660875843366183932, 29203826183438553070884, 190532364093474078966872, 1244726956899863089810570, 8141639269062000755364430, 53314139631682313794324013, 349486076564183688619590218, 2293199005413647360079515420, 15060813402323636201444709240, 98997215041442655314479356281, 651239576384893874930191938026, 4287255209271566144062267532730, 28243466155565219000565456149716, 186182048789894859449130087801643, 1228064947854915492876566222109484, 8104990717951877141197461897819508, 53520053456631812342974671874329136, 353589763445300714395883920268554702, 2337164461447314935354909652835383768, 15455161719853409161863422124692695375, 102244890081205806586889337431176976130, 676679951936069264254621030977253136571, 4480115506784939739694202220294797853116, 29672253259103511911934380736774387503237, 196588930615397226908899023088340969197018, 1302888217720973317317027294449087876609669, 8637492087547200882982580806125030127194664, 57278796496845655773183220628338133084141520, 379943967038559843075614203171320194362391202, 2520918418642170439256886796824582879264348554, 16730390768521966840289356431421095133934290652, 111059638050842816314416065586652004057215287851, 737402200587461792701934684745481040684809682072, 4897179589453980205635190085295577270830347650957, 32529451836206393186793356441177060831941126283854, 216118779988202126517355242312821149338050447946261, 1436115880361059583101918839320484949901010039559700, 9544739047555264534609646488146662666154742420711270, 63447251671018706208562039140252474695167799150851440, 421825200028003528505068907462048241238043886170968738, 2804917709942885515892469720455225221233874863799618704, 18654032718014509209636436842607532743654389220655063276, 124075950915785763826180700306821040471219612735708902270, 825395628960759012106613317761974063500899355979448179581, 5491537215855645756085744394857204202144058366446577245182, 36541012560494961273275528606064535712387611112726148358911, 243175539484614111290858519760436275403555657975213901534564, 1618489019984137647028971657643889036149880724271794903489539, 10773285896848573008406052934343686914312295613828295095702870, 71718841961807716576631428286621011327158123207354154474812239, 477488808638593900811036956679234976498204986008842792193032934, 3179334682329215131346025613301645346791753728178426391111632939, 21171458557506057137941482235172811309544708478985552480869330132, 140995491614375175061161047838529818651060189513403776112463822451, 939070285377277986739610033559490565210156390822824247016680242374, 6255009498319965390396326475768838690095202227096548648213252396394, 41667120973996041543539017945441230536030139855699474030761001839794, 277583317984056905901596121074232046961083667279062732995031287819940, 1849380793016620290404600941405666181507301005919384690195197298766956, 12322285061079400367161824257304122462001684685794482132169749745648861, 82108280534936004896471511375380864544228119480151967914853069204270014, 547157528893590651675384530361719361843352879146441226065141046690578846, 3646418261208038137091845416621467610454450910216112277163537394128929068, 24302350319352891323941637596006052017420431462308387452284760983296568819, 161978291435707151034988715386290704044799222133246519609814259951900783958, 1079670374008464432430576353845119068388821106844396181279052363822283373636, 7196983701186798348292920693011466637831803020249562727957179760948695911606, 47977098865816650043400484101881513363324373119826638563983930921389153103686, 319845891110690242563282948237438210557639937884928588783073097409534175994166, 2132407151353123722199933591294317964052920602239141798641901025289095588432183, 14217436903491868046845762512244277858246441507189186934346074520853074677463728
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/24208/
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[4,x]
F[3,x] = x
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[8,x,k[0]]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x,k[0]] = F[10,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,1,k[0]]
F[11,x,k[0],k[1]] = F[12,x,k[0]*k[1],k[1]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[28,x,k[0],k[1]]+F[30,x,k[1],k[0]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[3,x]
F[14,x,k[0],k[1]] = F[15,x,1,k[0],k[1]]
F[15,x,k[0],k[1],k[2]] = F[1,x]+F[16,x,k[0],k[1],k[2]]+F[18,x,k[0],k[1],k[2]]+F[22,x,k[1],k[0],k[2]]+F[26,x,k[2],k[0],k[1]]
F[16,x,k[0],k[1],k[2]] = F[17,x,k[0],k[1],k[2]]*F[3,x]
F[17,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[15,x,k[0],k[1],k[2]]*k[0]-F[15,x,1,k[1],k[2]])
F[18,x,k[0],k[1],k[2]] = F[19,x,k[0],k[1],k[2]]*F[9,x,k[0]]
F[19,x,k[0],k[1],k[2]] = (F[20,x,k[0],k[1]]*k[1]-F[20,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[20,x,k[0],k[1]] = (F[21,x,k[0],1]*k[0]-F[21,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[21,x,k[0],k[1]] = F[12,x,k[0],k[0]*k[1]]
F[22,x,k[0],k[1],k[2]] = F[23,x,k[0],k[2],k[1]]
F[23,x,k[0],k[1],k[2]] = F[24,x,k[1]]*F[25,x,k[2],k[0]]*F[9,x,k[0]]
F[24,x,k[0]] = F[1,x]+F[9,x,k[0]]
F[25,x,k[0],k[1]] = (-F[11,x,1,k[1]]*k[1]+F[11,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[26,x,k[0],k[1],k[2]] = F[27,x,k[0],k[1],k[2]]
F[27,x,k[0],k[1],k[2]] = F[15,x,k[1],k[2],k[0]]*F[24,x,k[0]]*F[9,x,k[0]]
F[28,x,k[0],k[1]] = F[29,x,k[0],k[1]]
F[29,x,k[0],k[1]] = F[10,x,k[0]]*F[24,x,k[1]]*F[9,x,k[0]]
F[30,x,k[0],k[1]] = F[31,x,k[0],k[1]]
F[31,x,k[0],k[1]] = F[12,x,k[1],k[0]]*F[24,x,k[0]]*F[9,x,k[0]]
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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{5}\! \left(x , y_{0}\right)+F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = y_{0} x
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , 1, y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{1}, y_{0}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , 1, y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{22}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{26}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{3}\! \left(x \right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{0} F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{15}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{9}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{20}\! \left(x , y_{0}, y_{1}\right)-y_{2} F_{20}\! \left(x , y_{0}, y_{2}\right)}{-y_{2}+y_{1}}
F_{20}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{21}\! \left(x , y_{0}, 1\right)-y_{1} F_{21}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{23}\! \left(x , y_{0}, y_{2}, y_{1}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{1}\right) F_{25}\! \left(x , y_{2}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{24}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{9}\! \left(x , y_{0}\right)
F_{25}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} F_{11}\! \left(x , 1, y_{1}\right)-y_{0} F_{11}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{15}\! \left(x , y_{1}, y_{2}, y_{0}\right) F_{24}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{29}\! \left(x , y_{0}, y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , y_{0}\right) F_{24}\! \left(x , y_{1}\right) F_{9}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{31}\! \left(x , y_{0}, y_{1}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{1}, y_{0}\right) F_{24}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\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)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_8(x, k_0))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x, k_0), F_10(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, 1, k_0))
Eq(F_11(x, k_0, k_1), F_12(x, k_0*k_1, k_1))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_28(x, k_0, k_1) + F_30(x, k_1, k_0))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_3(x))
Eq(F_14(x, k_0, k_1), F_15(x, 1, k_0, k_1))
Eq(F_15(x, k_0, k_1, k_2), F_1(x) + F_16(x, k_0, k_1, k_2) + F_18(x, k_0, k_1, k_2) + F_22(x, k_1, k_0, k_2) + F_26(x, k_2, k_0, k_1))
Eq(F_16(x, k_0, k_1, k_2), F_17(x, k_0, k_1, k_2)*F_3(x))
Eq(F_17(x, k_0, k_1, k_2), (k_0*F_15(x, k_0, k_1, k_2) - F_15(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_18(x, k_0, k_1, k_2), F_19(x, k_0, k_1, k_2)*F_9(x, k_0))
Eq(F_19(x, k_0, k_1, k_2), (-k_1*F_20(x, k_0, k_1) + k_2*F_20(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_20(x, k_0, k_1), (-k_0*F_21(x, k_0, 1) + k_1*F_21(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_21(x, k_0, k_1), F_12(x, k_0, k_0*k_1))
Eq(F_22(x, k_0, k_1, k_2), F_23(x, k_0, k_2, k_1))
Eq(F_23(x, k_0, k_1, k_2), F_24(x, k_1)*F_25(x, k_2, k_0)*F_9(x, k_0))
Eq(F_24(x, k_0), F_1(x) + F_9(x, k_0))
Eq(F_25(x, k_0, k_1), (-k_0*F_11(x, k_0/k_1, k_1) + k_1*F_11(x, 1, k_1))/(-k_0 + k_1))
Eq(F_26(x, k_0, k_1, k_2), F_27(x, k_0, k_1, k_2))
Eq(F_27(x, k_0, k_1, k_2), F_15(x, k_1, k_2, k_0)*F_24(x, k_0)*F_9(x, k_0))
Eq(F_28(x, k_0, k_1), F_29(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), F_10(x, k_0)*F_24(x, k_1)*F_9(x, k_0))
Eq(F_30(x, k_0, k_1), F_31(x, k_0, k_1))
Eq(F_31(x, k_0, k_1), F_12(x, k_1, k_0)*F_24(x, k_0)*F_9(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "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.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "col_placements_tracked_fusion", "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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