10243_10342_10432_20143_20341_20431_21043_30142_30241_31042
Counting sequence:
1, 1, 2, 6, 24, 110, 543, 2818, 15189, 84367, 480216, 2789318, 16480115, 98794581, 599722994, 3680560333, 22806072289, 142523281826, 897474333514, 5690131537662, 36299352846623, 232864900705304, 1501491698157444, 9726757528483323, 63281224117528623, 413330974442534052, 2709620027104062330, 17823429537883254175, 117609856974671469364, 778347064284277051725, 5165312446991982703113, 34366726307816424425653, 229207836998156323315939, 1532173960493287903797513, 10264008443729395948630144, 68897589474004169066405276, 463362868045489853141295260, 3121939591387560910814640561, 21070417759105127996903526265, 142439217419838361803602820675, 964403920030803882048945515693, 6539265854933984225242313287992, 44402724380563245072764954481642, 301906776109524744534009365844202, 2055382367118364446456418721400155, 14010206415988339914027382282771789, 95610539783575137279492212941036342, 653213209542393128837638318412555256, 4467576950984188664837681614512658097, 30587090877847787647963449537169748704, 209621403548524612751655500702769055212, 1437962947307286784436940489910912479437, 9873216003954378430287926228379653724920, 67850583420366826381233829210110393788258, 466679246487659578103663983723706650432331, 3212477169495738797023325298412996164624886, 22131236673696375495199535780113299943237665, 152582052167162881638414108849462590878985096, 1052742202258816235855543513249973527018556454, 7268598378716503774223700486662916231385154689, 50220282121980610513887301365464989226762867171, 347214404446190980354903094913103080072038803417, 2402133671278532461071637592897175389317862647346, 16629095829453405480191298536105658697396393441423, 115187065895135987361345584262089296538104986159765, 798351932906304922146388182398050350534470017565915, 5536470166959601369414698606295904895203597735765934, 38415999494431615911581226697055202551220439083365776, 266701152422219652164147312089127498232320646239051158, 1852526905265917340406596251115139072118157198231108112, 12874329250342408335547796933363299604315435724676359853, 89515656780423188104300352440488848536910777603004887992, 622704204899312382295312726308996916126689458457960019685, 4333784793853644163328426858259634967598621785631123218691, 30175203036737358038997194014452133378210789384838776254796, 210196345821534255074544635021918789644865778692208313428694, 1464829954966879060322094015838513039766941485828137611317487, 10212487443727089415567659966670943635089264103771330564156828, 71228450553468899242640203325732230423277032917992461270002812, 496991130054249850768547404648161811398148934226859262750306900, 3469066811173272813460527800250701588267593533312147043713577121, 24223753587427386576068519297006064031008038957149283185552389440, 169211930437847239375475608583532970841891063703258619393607404764, 1182435449535182472591712613067464647818077499336593625157971898105, 8265652014320197797996920193109794571969386657683455440868579316786, 57799812728090734202027527915388470335552282617489715932134732575190, 404316932857684970692625737466328361395228228145914506316299479266453, 2829178042420630367454066199280866652070454565752388125696995192297702, 19803331417667284999664381775977459967844681363378921985703953385076107, 138660495033236153330345030023084567595282395781003313273717558780433053, 971182257668753056772708959207382400796559657984288977894688967909948714, 6804235293745607838432174467769811815736447424516743874049803117989531087, 47685427307190467579304628497948931953553129936084696638810885847429284631, 334285145033342816859338264220950172431484180573217939840332718165540406589, 2344071632706786980488517040804242059329213657887991288139664526954750613402, 16441616875431286537731527538790519792508852767870181428052938868436118214192, 115354763444373870874634018273364681172418560427823792226249731835025345174647, 809545946913561433652711315587688215884253215510219966059027835484436274329437, 5682770318590222312443091112306117185792566241149721696630339361512858331794636, 39901486468826885837053388279651060997590804069503111519531602136559604947750164, 280237483678704217100516611517202555964804888082066799179666467234113038742987208
Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/24806/
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[30,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[30,x]*F[7,x]
F[7,x] = F[52,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x,1]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[30,x]
F[13,x,k[0]] = F[14,x,k[0]]+F[51,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]+F[49,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[47,x,k[0]]+F[48,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[1,x]+F[18,x,k[0]]+F[20,x,k[0]]
F[18,x,k[0]] = F[17,x,k[0]]*F[19,x,k[0]]
F[19,x,k[0]] = k[0]*x
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]*F[30,x]
F[22,x,k[0]] = F[23,x,k[0]]+F[4,x]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]*F[46,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]+F[34,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]+F[31,x,k[0]]
F[27,x,k[0]] = F[16,x,k[0]]+F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[25,x,k[0]]*F[30,x]
F[30,x] = x
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[27,x,k[0]]*F[30,x]*F[33,x,k[0]]
F[33,x,k[0]] = F[11,x,k[0]]+F[22,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[30,x]*F[36,x,k[0]]
F[37,x,k[0]] = F[36,x,k[0]]*F[46,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]
F[39,x,k[0]] = F[38,x,k[0]]+F[7,x]
F[39,x,k[0]] = F[40,x,k[0]]+F[43,x,k[0]]
F[40,x,k[0]] = F[22,x,k[0]]+F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]
F[42,x,k[0]] = (F[11,x,k[0]]*k[0]-F[11,x,1])/(-1+k[0])
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[30,x]*F[4,x]*F[45,x,k[0]]
F[45,x,k[0]] = (F[33,x,k[0]]*k[0]-F[33,x,1])/(-1+k[0])
F[46,x,k[0]] = k[0]*x
F[47,x,k[0]] = F[15,x,k[0]]*F[46,x,k[0]]
F[48,x,k[0]] = F[13,x,k[0]]*F[30,x]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[15,x,k[0]]*F[30,x]*F[33,x,k[0]]
F[51,x,k[0]] = F[34,x,k[0]]
F[52,x] = F[53,x]
F[53,x] = F[30,x]*F[4,x]*F[54,x]
F[54,x] = F[33,x,1]
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_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{30}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{52}\! \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_{10}\! \left(x \right) = F_{11}\! \left(x , 1\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{47}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = y x
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{46}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = x
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{30}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{46}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{7}\! \left(x \right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = -\frac{-F_{11}\! \left(x , y\right) y +F_{11}\! \left(x , 1\right)}{-1+y}
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = -\frac{-y F_{33}\! \left(x , y\right)+F_{33}\! \left(x , 1\right)}{-1+y}
F_{46}\! \left(x , y\right) = y x
F_{47}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{46}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{30}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{33}\! \left(x , 1\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_30(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_30(x)*F_7(x))
Eq(F_7(x), F_52(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x, 1))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_30(x))
Eq(F_13(x, k_0), F_14(x, k_0) + F_51(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0) + F_49(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_47(x, k_0) + F_48(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_1(x) + F_18(x, k_0) + F_20(x, k_0))
Eq(F_18(x, k_0), F_17(x, k_0)*F_19(x, k_0))
Eq(F_19(x, k_0), k_0*x)
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0)*F_30(x))
Eq(F_22(x, k_0), F_23(x, k_0) + F_4(x))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0)*F_46(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0) + F_34(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0) + F_31(x, k_0))
Eq(F_27(x, k_0), F_16(x, k_0) + F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_25(x, k_0)*F_30(x))
Eq(F_30(x), x)
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_27(x, k_0)*F_30(x)*F_33(x, k_0))
Eq(F_33(x, k_0), F_11(x, k_0) + F_22(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_30(x)*F_36(x, k_0))
Eq(F_37(x, k_0), F_36(x, k_0)*F_46(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0))
Eq(F_39(x, k_0), F_38(x, k_0) + F_7(x))
Eq(F_39(x, k_0), F_40(x, k_0) + F_43(x, k_0))
Eq(F_40(x, k_0), F_22(x, k_0) + F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_42(x, k_0), (-k_0*F_11(x, k_0) + F_11(x, 1))/(1 - k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_30(x)*F_4(x)*F_45(x, k_0))
Eq(F_45(x, k_0), (-k_0*F_33(x, k_0) + F_33(x, 1))/(1 - k_0))
Eq(F_46(x, k_0), k_0*x)
Eq(F_47(x, k_0), F_15(x, k_0)*F_46(x, k_0))
Eq(F_48(x, k_0), F_13(x, k_0)*F_30(x))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_15(x, k_0)*F_30(x)*F_33(x, k_0))
Eq(F_51(x, k_0), F_34(x, k_0))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_30(x)*F_4(x)*F_54(x))
Eq(F_54(x), F_33(x, 1))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_symmetries", "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", "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}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "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}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": 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}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
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