02143_02413_02431_04213_04231_04321_40213_40231_40321
Counting sequence:
1, 1, 2, 6, 24, 111, 546, 2758, 14110, 72687, 375998, 1950212, 10134024, 52730484, 274647566, 1431611637, 7466906982, 38964752623, 203414137624, 1062281354847, 5549126721642, 28994684041417, 151532627312524, 792092520684134, 4141117956076628, 21653232078212560, 113235882230509216, 592236813901137134, 3097785561739209688, 16204933150179422865, 84777183595919660830, 443550401486916670097, 2320791075067221918148, 12143821660990598370241, 63547502234004267077968, 332554733974781436013550, 1740393059283216108655550, 9108551782599752906429442, 47672453817773750206694184, 249517169109863013796156908, 1306010969256820680596348938, 6836054450035525358717923087, 35782892957644502892892967946, 187307721846489504721307598964, 980494923099548007758655310556, 5132673876467823970606514325196, 26868903045712743286387718956158, 140657696516715928107636962160445, 736349128928809692551805144493994, 3854874383621455034214041233903678, 20180985580480561897365002014485084, 105652494717637259681233401584193895, 553123328477090108533065994512431864, 2895800623770843482472896271868169718, 15160707192702274047555935377719053690, 79373233141315846408600819678354413079, 415558531693566267301305630439189515518, 2175672854024371283734194949542650665581, 11390898941484286128875675277418348222478, 59638292138009525124883553830592520080112, 312244635657338627095684882239328818745276, 1634809580365865201658651231311742240902052, 8559365835277665275141830978112714401828466, 44814449955968315914375971426883840700506548, 234636985675625241261294024486353082593947372, 1228504223284874423010560718967430177388803681, 6432184508127564063723228640703071025079825370, 33677657364983249781163212412286309978001509883, 176330194884069164134075274180644962601190093260, 923236220286402970184784376943795928291488812913, 4833928501834120045415794131505997324315223751486, 25309803112189573084181791639817057481615196393078, 132519072622525177987707357778599735250256406571214, 693855464579885251221414175176397713360833475866966, 3632959645541605288010209481250220007081659458618478, 19021861155468377462652177511540390373766949190894734, 99596999548193401851030814373454180463659910578413774, 521483128985954303545631609338323887486577226920702585, 2730454724797522770880054374842545688564858853971266316, 14296520752049672895760491140751815644138350344602495978, 74855955294986204667404387373912998712878633843788887536, 391943018846944236456413587172397731132754527647089119601, 2052201732713991619558385515319029456271084516073083081914, 10745278390589920959743629901146182152210151404534297272817, 56262077675211392281186194629741637671943227808967471593148, 294587491383838511175519948473973995114810953389348532017147, 1542457660440001561788298166354342817923557799230827190102882, 8076302707229085402704047626971001797547601748296014583276146, 42287526911356370146867555826946999526863619116894861533630290, 221417694922811226216770908500975196071112070224805344956764778, 1159344966880362860011989400674785451632441432520360717860463950, 6070344439826239754589452497000220300074526952421801549413414740, 31784418210784421793643981681220947061920011083134065141261547902, 166423809873227736224588806962352689383239144707590778960727351429, 871398681345047449260983244690465727792731167723674545053140473808, 4562664825633288748709660797916585379548346273456563940809708713119, 23890236561423477256543236187710939717434434434423201585622891661214, 125089983661688483037912748793526898561831182546974196241072698790790, 654975131869908260513039100878281003338658449286813749185646509227166, 3429472020960198364336563456166809038767735190953472181474626625492654, 17956838803867865062307341882479989240601733649275870328145358453033854
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24194/
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[7,x]
F[3,x] = F[4,x,1]
F[4,x,k[0]] = F[1,x]+F[5,x,k[0]]+F[8,x,k[0]]
F[5,x,k[0]] = F[6,x,k[0]]*F[7,x]
F[6,x,k[0]] = 1/(-1+k[0])*(F[4,x,k[0]]*k[0]-F[4,x,1])
F[7,x] = x
F[8,x,k[0]] = F[17,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[10,x,1,k[0]]*k[0]-F[10,x,1/k[0],k[0]])
F[10,x,k[0],k[1]] = F[11,x,k[0]*k[1],k[1]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[18,x,k[0],k[1]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]
F[13,x,k[0],k[1]] = F[11,x,k[0],k[1]]*F[14,x,k[0]]*F[17,x,k[0]]
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[14,x,k[0]]^2*F[17,x,k[0]]
F[17,x,k[0]] = k[0]*x
F[18,x,k[0],k[1]] = F[17,x,k[1]]*F[19,x,k[0],k[1]]
F[19,x,k[0],k[1]] = F[1,x]+F[20,x,k[0],k[1]]+F[22,x,k[0],k[1]]+F[26,x,k[1]]
F[20,x,k[0],k[1]] = F[21,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[14,x,k[0]]*F[17,x,k[0]]*F[19,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[23,x,k[0],k[1]]
F[23,x,k[0],k[1]] = F[17,x,k[1]]*F[24,x,k[0],k[1]]*F[25,x,k[1]]
F[24,x,k[0],k[1]] = (F[14,x,k[0]]*k[0]-F[14,x,k[1]]*k[1])/(-k[1]+k[0])
F[25,x,k[0]] = F[10,x,1,k[0]]
F[26,x,k[0]] = F[27,x,1,k[0]]
F[27,x,k[0],k[1]] = F[18,x,k[0]*k[1],k[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_{7}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{5}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{5}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{6}\! \left(x , y\right) = \frac{y F_{4}\! \left(x , y\right)-F_{4}\! \left(x , 1\right)}{-1+y}
F_{7}\! \left(x \right) = x
F_{8}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = \frac{y F_{10}\! \left(x , 1, y\right)-F_{10}\! \left(x , \frac{1}{y}, y\right)}{-1+y}
F_{10}\! \left(x , y , z\right) = F_{11}\! \left(x , y z , z\right)
F_{11}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{18}\! \left(x , y , z\right)
F_{12}\! \left(x , y , z\right) = F_{13}\! \left(x , y , z\right)
F_{13}\! \left(x , y , z\right) = F_{11}\! \left(x , y , z\right) F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{14}\! \left(x , y\right)^{2} F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = y x
F_{18}\! \left(x , y , z\right) = F_{17}\! \left(x , z\right) F_{19}\! \left(x , y , z\right)
F_{19}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{20}\! \left(x , y , z\right)+F_{22}\! \left(x , y , z\right)+F_{26}\! \left(x , z\right)
F_{20}\! \left(x , y , z\right) = F_{21}\! \left(x , y , z\right)
F_{21}\! \left(x , y , z\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{19}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = F_{23}\! \left(x , y , z\right)
F_{23}\! \left(x , y , z\right) = F_{17}\! \left(x , z\right) F_{24}\! \left(x , y , z\right) F_{25}\! \left(x , z\right)
F_{24}\! \left(x , y , z\right) = \frac{y F_{14}\! \left(x , y\right)-z F_{14}\! \left(x , z\right)}{-z +y}
F_{25}\! \left(x , y\right) = F_{10}\! \left(x , 1, y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , 1, y\right)
F_{27}\! \left(x , y , z\right) = F_{18}\! \left(x , y z , z\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_7(x))
Eq(F_3(x), F_4(x, 1))
Eq(F_4(x, k_0), F_1(x) + F_5(x, k_0) + F_8(x, k_0))
Eq(F_5(x, k_0), F_6(x, k_0)*F_7(x))
Eq(F_6(x, k_0), (k_0*F_4(x, k_0) - F_4(x, 1))/(k_0 - 1))
Eq(F_7(x), x)
Eq(F_8(x, k_0), F_17(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_10(x, 1, k_0) - F_10(x, 1/k_0, k_0))/(k_0 - 1))
Eq(F_10(x, k_0, k_1), F_11(x, k_0*k_1, k_1))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_18(x, k_0, k_1))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), F_11(x, k_0, k_1)*F_14(x, k_0)*F_17(x, k_0))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_14(x, k_0)**2*F_17(x, k_0))
Eq(F_17(x, k_0), k_0*x)
Eq(F_18(x, k_0, k_1), F_17(x, k_1)*F_19(x, k_0, k_1))
Eq(F_19(x, k_0, k_1), F_1(x) + F_20(x, k_0, k_1) + F_22(x, k_0, k_1) + F_26(x, k_1))
Eq(F_20(x, k_0, k_1), F_21(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_14(x, k_0)*F_17(x, k_0)*F_19(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), F_23(x, k_0, k_1))
Eq(F_23(x, k_0, k_1), F_17(x, k_1)*F_24(x, k_0, k_1)*F_25(x, k_1))
Eq(F_24(x, k_0, k_1), (-k_0*F_14(x, k_0) + k_1*F_14(x, k_1))/(-k_0 + k_1))
Eq(F_25(x, k_0), F_10(x, 1, k_0))
Eq(F_26(x, k_0), F_27(x, 1, k_0))
Eq(F_27(x, k_0, k_1), F_18(x, k_0*k_1, k_1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "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": "row_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, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "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": [4, 0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 3, 1], "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]]}], "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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "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], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [4, 0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [4, 0, 3, 2, 1], "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], [2, 0]]}, {"patt": [4, 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