02143_02413_02431_03142_04132_13042_14032_24031_243051_350214_354021
Counting sequence:
1, 1, 2, 6, 24, 112, 556, 2811, 14234, 71808, 360568, 1803100, 8988924, 44719588, 222221416, 1103827306, 5484124128, 27265300504, 135695994964, 676228846370, 3374996253420, 16871826671280, 84488005896720, 423828619074900, 2129868537725916, 10722045181336524, 54069490551238232, 273123283923924504, 1381895139953246752, 7002883275718347136, 35541688336255218480, 180647403012233283203, 919455726172646988090, 4686067342038215532336, 23913248538427983545208, 122178707289650496966292, 624963820821955444060452, 3200318453283258297871244, 16405450465384748846660792, 84181871927845282867228764, 432378797862811334122813344, 2222831972055486917356802032, 11437403053845363749807804536, 58899268448681103407163622836, 303555547439382530149506449080, 1565659384626111501355028004640, 8081149620610951470516996413600, 41740004610920286612678339594180, 215736098958998707891084506184860, 1115764022631467511548589995994108, 5774175525652720913267105062395768, 29899589413324650326793361730335560, 154913115106561534201438298708190624, 803062820700942350032189403158740928, 4165243376754865412031716158412951824, 21614859129539675928365719180909154396, 112221915800229579164695966925207110152, 582919630488347006484183728824845965184, 3029272165440713682494085740819192274272, 15749245663296240958680704482303549966960, 81915605574741258115142170431478756031344, 426238674926221691959413098334784178020752, 2218771434664933644191998251796981370689440, 11554209833956252908162465301081283055465594, 60190871576791200953501342041629392792139648, 313674114579202405468595777077290549727757688, 1635232823674933541307012971319037563265809204, 8527638727071607925713794389206114742953740282, 44485849760166393240388773606545096042462838972, 232142522207903768098956977042758633431750319920, 1211778401055336318374185874314737452702110146000, 6327375042604192212008839830985614360137608207980, 33048528697243240771890026027302959435745003972740, 172665407591907316759109938401940532761702119145140, 902359966693443589998417302899480748170081244321064, 4717070061486652434937080086006708867767399542946824, 24664921725716306220904909677802687740795338166569952, 129002779503380490080370861029722613551661339806430976, 674881346993710227256222753796967614878297438279754256, 3531523027199552887489397170102925933963309563924886202, 18484182771335556777289593641529987481808173845940453196, 96769721944913881882356289257405202813811581198473987552, 506730781842220588450954855580389970933658320784394260496, 2654063148741919517266809268584094215819548591036370947896, 13903978620058696180789483283078303640427886885277273013464, 72854870204233146824269075523014419544784854614620130219272, 381827853477620910574498023728178363451063488860411335579344, 2001539100284588949085356589691805956344798207017334832543832, 10494119674117210195091118866154355519687553250928091475936192, 55031516629252236772826526946469382782366780076152200080930784, 288641401423390060850678853460514535653125935728587076844423984, 1514208362212137286205357377221993046877907933518774973934573352, 7944943037268691450298626800153189252383443828274597054971928816, 41693886724777749615495716508508565816629854564394069456952483136, 218841051234442653417032951611786031127586464208805114900228948800, 1148837065275898483573687356229703867271740482282071913774179944100, 6031978600222275517284541746520807464720816496482662272664913807900, 31676075510406231041870821289612452035010790051609779031357387271900, 166368742678540194430882713253306478399414513227091433373898403132600, 873935726391043647173204918536777034771501320020790418480548127802600, 4591486331353551969934518814059301940973444011516674578916051045437600
Specification 1
Strategy pack name: row_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/24241/
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,k[0]]+F[5,x,k[0]]
F[12,x,k[0]] = F[11,x,k[0]]+F[20,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0],1]
F[13,x,k[0],k[1]] = 1/(-1+k[0])*(F[14,x,1,k[0],k[1]]*k[0]-F[14,x,1/k[0],k[0],k[1]])
F[14,x,k[0],k[1],k[2]] = F[15,x,k[0]*k[1],k[1]*k[2]]
F[15,x,k[0],k[1]] = F[1,x]+F[16,x,k[0],k[1]]+F[19,x,k[1],k[0]]
F[16,x,k[0],k[1]] = F[17,x,k[0],k[1]]*F[9,x,k[0]]
F[17,x,k[0],k[1]] = F[18,x,1,k[0],k[1]]
F[18,x,k[0],k[1],k[2]] = (F[14,x,k[0],k[1],1]*k[1]-F[14,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[19,x,k[0],k[1]] = F[15,x,k[1],k[0]]*F[9,x,k[0]]
F[20,x,k[0]] = F[15,x,1,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 , y_{0}\right)+F_{5}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right)+F_{20}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}, 1\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{14}\! \left(x , 1, y_{0}, y_{1}\right)-F_{14}\! \left(x , \frac{1}{y_{0}}, y_{0}, y_{1}\right)}{-1+y_{0}}
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{15}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{19}\! \left(x , y_{1}, y_{0}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , 1, y_{0}, y_{1}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{14}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{14}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{1}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = F_{15}\! \left(x , 1, 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, k_0) + F_5(x, k_0))
Eq(F_12(x, k_0), F_11(x, k_0) + F_20(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0, 1))
Eq(F_13(x, k_0, k_1), (k_0*F_14(x, 1, k_0, k_1) - F_14(x, 1/k_0, k_0, k_1))/(k_0 - 1))
Eq(F_14(x, k_0, k_1, k_2), F_15(x, k_0*k_1, k_1*k_2))
Eq(F_15(x, k_0, k_1), F_1(x) + F_16(x, k_0, k_1) + F_19(x, k_1, k_0))
Eq(F_16(x, k_0, k_1), F_17(x, k_0, k_1)*F_9(x, k_0))
Eq(F_17(x, k_0, k_1), F_18(x, 1, k_0, k_1))
Eq(F_18(x, k_0, k_1, k_2), (-k_1*F_14(x, k_0, k_1, 1) + k_2*F_14(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_19(x, k_0, k_1), F_15(x, k_1, k_0)*F_9(x, k_0))
Eq(F_20(x, k_0), F_15(x, 1, 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": 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_and_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, 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, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 5, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 5, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 5, 4, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 3], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 3], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 3], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, 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