01324_02314_03214_10324_12304_13204_20314_21304
Counting sequence:
1, 1, 2, 6, 24, 112, 570, 3062, 17066, 97700, 570862, 3389812, 20394106, 124034760, 761292536, 4709264410, 29328534118, 183735748344, 1157070304524, 7320431897486, 46506419726168, 296557419720726, 1897451404446330, 12177717356311514, 78375302559831418, 505719712071758448, 3270914237978461438, 21202086645319360014, 137710953249161015952, 896141346003070435684, 5841802136842125821214, 38144258995681891996188, 249446890588493308120748, 1633625043009024548924276, 10713085597038669107251016, 70344555541153052654827672, 462454338496175668870204232, 3043694079490525249119321614, 20053978479375338306853334904, 132264468515800947864658344058, 873185455790511608795805137658, 5769918463811353750534660318186, 38160448752837691973102321282976, 252592228107029066056654331813832, 1673295125993202049495242742942852, 11093168883994131772851179947236494, 73596084978321679883758436284583454, 488603123036119562090272518056559198, 3245992357778103248702681269711146178, 21578266490369515066394289799991080056, 143533150272413703435036088922165333636, 955309184686320501030059429068392315634, 6361826810921850118595922070330486100554, 42389327952856956662417801804116005428634, 282591564192099318542769978015004280952042, 1884870367507711503681093944508151384375148, 12578113845957893303411157557117348018699720, 83975737169888873569330694920595363363747600, 560905005797791489686105371720119144373588388, 3748135434124628090824145289065299250885120378, 25056783606534258651339105627492535842889618406, 167576607147612644088792387430590365075653093492, 1121175809564769535581817099470147161261630886548, 7504137916896961337421070664215853087840123381732, 50244603723832292990945461671952535317307690406688, 336538367086694954164016307076337502056020732893464, 2254921975452174215487306653439300685296646115745774, 15113870119409785697860486324979703173819403753284370, 101335762084130598314306475917868289629864997117441982, 679655005783470701889748992086742858961462331561691344, 4559834239723083593858442544992941033132020928873914394, 30601346521737744660999029316875152514351017939399425430, 205427847672437393520881124875084253337555887768122989850, 1379437078822297286853050405617833129336700555668473525726, 9265415942682503037795386288275829936514692305921142503624, 62250833465498071281353812081918246822065263661453361410042, 418349787961675772979513626823802584560698439787389084912994, 2812192832409975637862359523489588735944867529170809634359718, 18908581295517937418333510653911749796973272495606292546479486, 127168148911899699674959671019887252873713590290655571972893334, 855461888618917582771808812365165922168759529394219091287678182, 5756033974495587762934492048657416866318440289199646898272060478, 38738602046616758848380451364147338979130978340198265652524687344, 260771478667033322716835202680167786167393709343335045718345957446, 1755777605624044717144075753091196440398507843779554439043254732928, 11824151716468238144189273823247087903972460569045500695527088690682, 79645167978979079592310071767458850792848105821853140500807094808736, 536581597994809725126800549239513281579012874740254446122374023823194, 3615738731560723994373282820972482839731473943502506380438928054433002, 24369202798128677177778011360121266186750199944991469888264471211895438, 164273219778874394510926328481909627335335019590452972273224720066161704, 1107571054383950982819444959111740983421204856602968793915455562593035496, 7468855851589500034590568110675595076444368173918629178755870837040963608, 50374707665894109061510157530791190566702883609842398162405462751450353542, 339817204153401674569540505592233892613948246130602493187040944821589352146, 2292719797589745171160248927133257706312153388114132737870065397003709760954, 15471338095901733128126242311521727080906215779300424929693087845292752551262, 104417809604708589912137920146160675732469099769669045270719426618401218907328, 704838568644347969710747999242666666749991295484841561804286093088556250450754, 4758518257470231561086742418202270468714455814781502642698172539232773280885486, 32130647364667724525722874174666415568807315225229966975148683112654491752667988
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24157/
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[1,x]+F[33,x]+F[5,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[31,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[10,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = 1/(-1+k[0])*(F[12,x,k[0]]*k[0]-F[12,x,1])
F[12,x,k[0]] = F[1,x]+F[13,x,k[0]]+F[29,x,k[0]]+F[8,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[3,x]
F[14,x,k[0]] = F[1,x]+F[15,x]+F[18,x]+F[19,x,k[0]]+F[27,x,k[0]]
F[15,x] = F[16,x]*F[3,x]
F[16,x] = F[17,x,1]
F[17,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[18,x] = F[13,x,1]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[26,x]*F[3,x]
F[21,x,k[0]] = 1/(-1+k[0])*(F[22,x,k[0]]*k[0]-F[22,x,1])
F[22,x,k[0]] = F[1,x]+F[23,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[22,x,k[0]]^2*F[25,x,k[0]]
F[25,x,k[0]] = k[0]*x
F[26,x] = F[12,x,1]
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[14,x,k[0]]*F[22,x,k[0]]*F[25,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[12,x,k[0]]*F[22,x,k[0]]*F[25,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[22,x,k[0]]*F[25,x,k[0]]*F[7,x,k[0]]
F[33,x] = F[26,x]*F[3,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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{33}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = -\frac{-y F_{7}\! \left(x , y\right)+F_{7}\! \left(x , 1\right)}{-1+y}
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y\right) = -\frac{-y F_{12}\! \left(x , y\right)+F_{12}\! \left(x , 1\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{29}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)+F_{18}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{3}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x , 1\right)
F_{17}\! \left(x , y\right) = -\frac{-y F_{7}\! \left(x , y\right)+F_{7}\! \left(x , 1\right)}{-1+y}
F_{18}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{26}\! \left(x \right) F_{3}\! \left(x \right)
F_{21}\! \left(x , y\right) = -\frac{-y F_{22}\! \left(x , y\right)+F_{22}\! \left(x , 1\right)}{-1+y}
F_{22}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{22}\! \left(x , y\right)^{2} F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = y x
F_{26}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{25}\! \left(x , y\right) F_{7}\! \left(x , y\right)
F_{33}\! \left(x \right) = F_{26}\! \left(x \right) F_{3}\! \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)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_33(x) + F_5(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_10(x, k_0) + F_31(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_10(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), (k_0*F_12(x, k_0) - F_12(x, 1))/(k_0 - 1))
Eq(F_12(x, k_0), F_1(x) + F_13(x, k_0) + F_29(x, k_0) + F_8(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_3(x))
Eq(F_14(x, k_0), F_1(x) + F_15(x) + F_18(x) + F_19(x, k_0) + F_27(x, k_0))
Eq(F_15(x), F_16(x)*F_3(x))
Eq(F_16(x), F_17(x, 1))
Eq(F_17(x, k_0), (-k_0*F_7(x, k_0) + F_7(x, 1))/(1 - k_0))
Eq(F_18(x), F_13(x, 1))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_26(x)*F_3(x))
Eq(F_21(x, k_0), (k_0*F_22(x, k_0) - F_22(x, 1))/(k_0 - 1))
Eq(F_22(x, k_0), F_1(x) + F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_22(x, k_0)**2*F_25(x, k_0))
Eq(F_25(x, k_0), k_0*x)
Eq(F_26(x), F_12(x, 1))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_14(x, k_0)*F_22(x, k_0)*F_25(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_12(x, k_0)*F_22(x, k_0)*F_25(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_22(x, k_0)*F_25(x, k_0)*F_7(x, k_0))
Eq(F_33(x), F_26(x)*F_3(x))
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, 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": [0, 3, 2, 1, 4], "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, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 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