01234_01324_02314_12304
Counting sequence:
1, 1, 2, 6, 24, 116, 634, 3770, 23850, 158298, 1091984, 7776312, 56877656, 425610184, 3248113394, 25217805778, 198767829018, 1587836221626, 12837005422636, 104904178607764, 865649527656056, 7206481018074864, 60478247435701200, 511299745405091696, 4352048830561205104, 37275656207278849776, 321120026846718219424, 2781244603980641263200, 24209103621928843878128, 211709492940044018283408, 1859484811758953767509506, 16398971858946799778535106, 145179130004744976915905882, 1289902403365481897323829146, 11499649900123855061832436580, 102850178614912457901062118604, 922661574712296056141951422208, 8300936144318575640542846510872, 74884970316130898064828171584236, 677307285779933587306202630509996, 6141086995962378188882146702588172, 55811288006979472720184046991838252, 508356750785921583393059676511008544, 4640241870954707234449058796650777424, 42442093799805790517351829528621891456, 388954261932575387595522126696512566144, 3571163121371710664577885518146343563696, 32847051988720037662696979128601667926960, 302640386419680617820684304950031125329520, 2793002192701210530370521812654201574730608, 25816744532028233215719993564344151876726944, 238996207921483868961743231663003048789080672, 2215720141114471576738744867297240570781338816, 20570724400122246097029467159195423817036530176, 191237370750798225447597152879289607952574591040, 1780177683597177618910365139102085931507248375104, 16592100743580086048604314492779176151966786791488, 154834557445402186722147808265252692518177438583872, 1446588286739837570932039211514041004495889146023616, 13530549899555496880620029848875054970700173289822144, 126696080154089326685870915695698694878936162817302496, 1187606860603370938885142794462891705101666846344266784, 11143697196502696945910523594694410624248415550932321570, 104669218568976744657140374415162781800939869472678155938, 984075393972099925991453519076804790277228648244447081818, 9260719327647634596810411900955666139869823735052732644826, 87227986655955104296107384255981345587656958339616227172116, 822337529132240016866941596818081831370121685859221986864252, 7759189778315044798765811729872252864505147851008169970087312, 73273001709772190031321445000185991771027400978115727285570408, 692504713099081211695530766155218340995860557239560602175401012, 6550023330034607164185345035293310433073750447609622927871439668, 62000465217155133877194108207974513366297320969828077477084149140, 587313580779021006754380649089610758023151545953585515528290089204, 5567490683143577253642804007136213863397710664118974700114279651104, 52814725026864394938183793055621070258408722274360583301874236139888, 501358806310127531440362224178186459879329050361409512548169867411088, 4762475034654027119768845489417928294845666632494297482203141714115376, 45268890143047804034730693460721407647678646196823628279235597542176508, 430569200208617211794061947318139387545872490898043481781603089945262652, 4097842129003939157650134977613372642454185245630137398161129703375410348, 39023844872388290245650879925946424201063975441197643758547880190834602092, 371844293276918610090987107141261137287197233089211542183448563999563887400, 3545212747171012746297676624995959861077001165315076030402485168765782182360, 33819540596916063744200233304765870248700944265537760958356143653292809691984, 322798594307398254390446770022641540236426761303002458210800601973298204050912, 3082681107318643995677183416001004047465427959734093237212121044714208386762176, 29454611248486622270428880863954361601892863235022837409271679319909142593463168, 281579212859806370084759608288415282393139367098883041698059382724520602398759552, 2693180931545547745469805825711501439299759821179584212901816241947660997081585792, 25771715223128610993310583105260965307301428219708612385065625379329815011629099264, 246734189676500761970011166332515208894456603023528871848164799773319168902251340544, 2363301190194684919024179324575451041708415226553700296965620116270328522064260658048, 22646870787371205292491578822854390888431348833720454507013550358356887830448512419968, 217116342222185533086696526643400066349716994040357118430317822210709080863428368341552, 2082418123791857028688929721915375729961545055951497867905933223083917656058291015536688, 19981611843650391473755568194619134911486057079803310888179719914692196255102281650304112, 191812293242816318923649888588791860575626896439653110267344889874475117898958890716886640, 1842052411780715601547374159507709553197257196615502986627949176644989163425911780393751136, 17697159117233384446687074650954195607317990486826802403648559245414196899824252365906363424, 170089562584342525577130077021002129832021647983515265937066712414897638785739520713042199296
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/24059/
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[1,x]+F[12,x,k[0],k[1]]+F[14,x,k[0],k[1]]+F[21,x,k[1],k[0]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[3,x]
F[13,x,k[0],k[1]] = 1/(k[0]*k[1]-1)*(F[11,x,k[0],k[1]]*k[0]*k[1]-F[11,x,1/k[1],k[1]])
F[14,x,k[0],k[1]] = F[15,x,k[0]*k[1],k[1]]
F[16,x,k[0],k[1]] = F[1,x]+F[15,x,k[0],k[1]]+F[17,x,k[0],k[1]]+F[19,x,k[1],k[0]]
F[16,x,k[0],k[1]] = (F[5,x,k[0]]*k[0]-F[5,x,k[1]]*k[1])/(-k[1]+k[0])
F[17,x,k[0],k[1]] = F[18,x,k[0],k[1]]*F[3,x]
F[18,x,k[0],k[1]] = 1/(-1+k[0])*(F[16,x,k[0],k[1]]*k[0]-F[16,x,1,k[1]])
F[19,x,k[0],k[1]] = F[20,x,k[1],k[0]]*F[9,x,k[0]]
F[20,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[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[11,x,k[1],k[0]]*F[23,x,k[0]]*F[9,x,k[0]]
F[23,x,k[0]] = F[1,x]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[23,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\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = \frac{F_{5}\! \left(x , y\right) y -F_{5}\! \left(x , 1\right)}{-1+y}
F_{8}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = y x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , 1, y\right)
F_{11}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{14}\! \left(x , y , z\right)+F_{21}\! \left(x , z , y\right)
F_{12}\! \left(x , y , z\right) = F_{13}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{13}\! \left(x , y , z\right) = \frac{F_{11}\! \left(x , y , z\right) y z -F_{11}\! \left(x , \frac{1}{z}, z\right)}{y z -1}
F_{14}\! \left(x , y , z\right) = F_{15}\! \left(x , y z , z\right)
F_{16}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y , z\right)+F_{17}\! \left(x , y , z\right)+F_{19}\! \left(x , z , y\right)
F_{16}\! \left(x , y , z\right) = \frac{F_{5}\! \left(x , y\right) y -F_{5}\! \left(x , z\right) z}{-z +y}
F_{17}\! \left(x , y , z\right) = F_{18}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{18}\! \left(x , y , z\right) = \frac{F_{16}\! \left(x , y , z\right) y -F_{16}\! \left(x , 1, z\right)}{-1+y}
F_{19}\! \left(x , y , z\right) = F_{20}\! \left(x , z , y\right) F_{9}\! \left(x , y\right)
F_{20}\! \left(x , y , z\right) = \frac{-F_{11}\! \left(x , 1, z\right) z +F_{11}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{21}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = F_{11}\! \left(x , z , y\right) F_{23}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{9}\! \left(x , y\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_1(x) + F_12(x, k_0, k_1) + F_14(x, k_0, k_1) + F_21(x, k_1, k_0))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_3(x))
Eq(F_13(x, k_0, k_1), (k_0*k_1*F_11(x, k_0, k_1) - F_11(x, 1/k_1, k_1))/(k_0*k_1 - 1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0*k_1, k_1))
Eq(F_16(x, k_0, k_1), F_1(x) + F_15(x, k_0, k_1) + F_17(x, k_0, k_1) + F_19(x, k_1, k_0))
Eq(F_16(x, k_0, k_1), (-k_0*F_5(x, k_0) + k_1*F_5(x, k_1))/(-k_0 + k_1))
Eq(F_17(x, k_0, k_1), F_18(x, k_0, k_1)*F_3(x))
Eq(F_18(x, k_0, k_1), (k_0*F_16(x, k_0, k_1) - F_16(x, 1, k_1))/(k_0 - 1))
Eq(F_19(x, k_0, k_1), F_20(x, k_1, k_0)*F_9(x, k_0))
Eq(F_20(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_21(x, k_0, k_1), F_22(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), F_11(x, k_1, k_0)*F_23(x, k_0)*F_9(x, k_0))
Eq(F_23(x, k_0), F_1(x) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_23(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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 2, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 3]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 4]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 3], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 3], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 4], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 3], [1, 3], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 3], [1, 4], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 2, 3], 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