01243_10243
Counting sequence:
1, 1, 2, 6, 24, 118, 672, 4256, 29176, 212586, 1625704, 12930160, 106242392, 897210996, 7756325952, 68422701792, 614341492144, 5602330498170, 51798365474872, 484856381630288, 4589003801130456, 43870126242653020, 423219224419273888, 4116816114087389056, 40351014094161799568, 398270701521760650532, 3956381717307865363920, 39537143015821042246400, 397295407341081007897328, 4012880896048851964224680, 40727106479677763596267520, 415202644844826924721722048, 4250728961878689581443559008, 43690010939373850999196353594, 450728376855738737831626514264, 4666260434066332493772730809712, 48468486264158181292068045772248, 505019740638526755815583983396812, 5277689845607409409811151289778656, 55309500034188545565118667203022656, 581185404041153074410888555260612816, 6122545274253288137560020488729839628, 64654531123152165904482912598964138416, 684331590351954534740691416955486811072, 7259207845623958622155043366816629487696, 77165701691116207791114535912970240585304, 821924689895427112326657392436331605851520, 8771525573906641927354066730250426169062592, 93781833822502230259289818924052986234951584, 1004453925523198797344585624468294416106523236, 10776512546803400741356685165349561021083212336, 115806890224931883707805990430290382319550790816, 1246439498313493301323811602872610821259201312752, 13435780462529380702636411756321508336695561725208, 145039125638400962019360545946096466771527544458560, 1567888013961437657535956862481024879091675947707392, 16971911176975697830440882172692824772597040788211104, 183955044251523887110958506743257885152573645688382984, 1996357699975430457998540636224984314861767285332251552, 21691629920058483856099126368400832249984808658827719424, 235969337853490959940095945236471440113145979465880594144, 2569873707782419079966680078007797461185951337075985700432, 28018499896955413825774593141264676730391702274038241556992, 305801562882344124657651285653929979855452476922117074384768, 3341040873334875053575627818611473740407820757100575298175168, 36539058825094504697595781621293237163628233444767533715278522, 399993786656491924656088654526542027456229349525588838885150104, 4382852810900705320337885807926450816213439322703148751271875760, 48068023626266055624388489042329382901026443275146738290324236760, 527642653160778191608505121282396256173114197552273478571251133484, 5796912942329191943665331396484563185333753279429521857060184888928, 63740634679529174500858896195203265233239128615781234120717822164160, 701436918547158001541949146905456846650020888169907742235448180975952, 7725094712507480741530473202117411454807385959612488921049169098301564, 85143731239504277695138996334928269957036495256795134065225053333449456, 939131280240077296599296953526985375512351545941062075932299717816387648, 10366117752709018981713398416099591636156939155235915038316289494688298128, 114502231105274669610232691261111143409213138300745414174093742262353128568, 1265644780083231520566312758803570846641097474571982048376210984752756209280, 13999166558378310385111131551727616308329643325869562729164351731818762771648, 154945038120345599363801827949515999311209183714311543744737027149151944089376, 1716055226348740661985903752103794527799172740549428140772470081055514511596620, 19017619363073064809458908442220378026182507504833196407875515424984598703441808, 210885053074136936917786628538625447327961033171585145631583292759883928205377632, 2339881666177334903897473345072553540436206522234554077044103528763347906449249104, 25977320252235805018088523276511430313085302024234666802539544053708553053465616200, 288563425875846964228480472112616335645493490180997691926611310065960225351025139904, 3207222076797027550558419615594366920386026270862635879660469079608436853451714648320, 35665811628254253696599387159730823367218872335314672899395496441610453015639703121120, 396830667610439411080131952809260936631134338706720375039474358661407826982995362995576, 4417568208231141620687873492283044945779887343669534352817372069455213005962828890518880, 49201831757579135098866128154332291207071090586161436926619145259155242063816845337155584, 548269976176356172809386709591808958171620807209928091823127355373178063308129118191764256, 6112490668089124557703693983518206464579345243230398841601532703817376872680156410860474672, 68178591088991637957104168413550545258104243488335006110267466889126734721657122844768357376, 760815866807074848483525085982193115859539134057498444852239015247578423414232922662021812864, 8493928860774824506331092904957446780467803504576820062109118611425540005344150544819030153536, 94870484870664659039607438761289229021233567514631923496442976694894092504154600930202840292324, 1060090914640057075633089114730419039363462892881434086131709313233185669735438810068701652521968, 11850611601359322355621907873646128446868521777871949258874270137649498922560175750415486745906784, 132531880417789777051436505065513685146279004048951026725853404983256898851417142523192318350981104
Specification 1
Strategy pack name: row_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/23972/
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[9,x]
F[3,x] = F[1,x]+F[27,x]+F[4,x]
F[4,x] = F[5,x]*F[9,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[11,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,k[0]]*F[9,x]
F[8,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[9,x] = x
F[10,x,k[0]] = F[8,x,k[0]]*F[9,x]
F[11,x,k[0]] = F[12,x,k[0]]*F[25,x,k[0]]
F[12,x,k[0]] = F[13,x,1,k[0]]
F[13,x,k[0],k[1]] = F[1,x]+F[14,x,k[0],k[1]]+F[16,x,k[0],k[1]]+F[17,x,k[0],k[1]]+F[26,x,k[0],k[1]]
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[9,x]
F[15,x,k[0],k[1]] = 1/(k[0]*k[1]-1)*(F[13,x,k[0],k[1]]*k[0]*k[1]-F[13,x,1/k[1],k[1]])
F[16,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[9,x]
F[17,x,k[0],k[1]] = F[18,x,k[0]*k[1],k[1]]
F[19,x,k[0],k[1]] = F[1,x]+F[18,x,k[0],k[1]]+F[20,x,k[0],k[1]]+F[22,x,k[0],k[1]]+F[23,x,k[0],k[1]]
F[19,x,k[0],k[1]] = (F[6,x,k[0]]*k[0]-F[6,x,k[1]]*k[1])/(-k[1]+k[0])
F[20,x,k[0],k[1]] = F[21,x,k[0],k[1]]*F[9,x]
F[21,x,k[0],k[1]] = 1/(-1+k[0])*(F[19,x,k[0],k[1]]*k[0]-F[19,x,1,k[1]])
F[22,x,k[0],k[1]] = F[21,x,k[0],k[1]]*F[9,x]
F[23,x,k[0],k[1]] = F[24,x,k[0],k[1]]*F[25,x,k[1]]
F[24,x,k[0],k[1]] = (-F[13,x,1,k[1]]*k[1]+F[13,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[25,x,k[0]] = k[0]*x
F[26,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[25,x,k[1]]
F[27,x] = F[5,x]*F[9,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_{9}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{9}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{11}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{8}\! \left(x , y\right) = \frac{F_{6}\! \left(x , y\right) y -F_{6}\! \left(x , 1\right)}{-1+y}
F_{9}\! \left(x \right) = x
F_{10}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , 1, y\right)
F_{13}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y , z\right)+F_{16}\! \left(x , y , z\right)+F_{17}\! \left(x , y , z\right)+F_{26}\! \left(x , y , z\right)
F_{14}\! \left(x , y , z\right) = F_{15}\! \left(x , y , z\right) F_{9}\! \left(x \right)
F_{15}\! \left(x , y , z\right) = \frac{F_{13}\! \left(x , y , z\right) y z -F_{13}\! \left(x , \frac{1}{z}, z\right)}{y z -1}
F_{16}\! \left(x , y , z\right) = F_{15}\! \left(x , y , z\right) F_{9}\! \left(x \right)
F_{17}\! \left(x , y , z\right) = F_{18}\! \left(x , y z , z\right)
F_{19}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y , z\right)+F_{20}\! \left(x , y , z\right)+F_{22}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)
F_{19}\! \left(x , y , z\right) = \frac{F_{6}\! \left(x , y\right) y -F_{6}\! \left(x , z\right) z}{-z +y}
F_{20}\! \left(x , y , z\right) = F_{21}\! \left(x , y , z\right) F_{9}\! \left(x \right)
F_{21}\! \left(x , y , z\right) = \frac{F_{19}\! \left(x , y , z\right) y -F_{19}\! \left(x , 1, z\right)}{-1+y}
F_{22}\! \left(x , y , z\right) = F_{21}\! \left(x , y , z\right) F_{9}\! \left(x \right)
F_{23}\! \left(x , y , z\right) = F_{24}\! \left(x , y , z\right) F_{25}\! \left(x , z\right)
F_{24}\! \left(x , y , z\right) = \frac{-F_{13}\! \left(x , 1, z\right) z +F_{13}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{25}\! \left(x , y\right) = y x
F_{26}\! \left(x , y , z\right) = F_{13}\! \left(x , y , z\right) F_{25}\! \left(x , z\right)
F_{27}\! \left(x \right) = F_{5}\! \left(x \right) F_{9}\! \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_9(x))
Eq(F_3(x), F_1(x) + F_27(x) + F_4(x))
Eq(F_4(x), F_5(x)*F_9(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_10(x, k_0) + F_11(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, k_0)*F_9(x))
Eq(F_8(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_9(x), x)
Eq(F_10(x, k_0), F_8(x, k_0)*F_9(x))
Eq(F_11(x, k_0), F_12(x, k_0)*F_25(x, k_0))
Eq(F_12(x, k_0), F_13(x, 1, k_0))
Eq(F_13(x, k_0, k_1), F_1(x) + F_14(x, k_0, k_1) + F_16(x, k_0, k_1) + F_17(x, k_0, k_1) + F_26(x, k_0, k_1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1)*F_9(x))
Eq(F_15(x, k_0, k_1), (k_0*k_1*F_13(x, k_0, k_1) - F_13(x, 1/k_1, k_1))/(k_0*k_1 - 1))
Eq(F_16(x, k_0, k_1), F_15(x, k_0, k_1)*F_9(x))
Eq(F_17(x, k_0, k_1), F_18(x, k_0*k_1, k_1))
Eq(F_19(x, k_0, k_1), F_1(x) + F_18(x, k_0, k_1) + F_20(x, k_0, k_1) + F_22(x, k_0, k_1) + F_23(x, k_0, k_1))
Eq(F_19(x, k_0, k_1), (-k_0*F_6(x, k_0) + k_1*F_6(x, k_1))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1), F_21(x, k_0, k_1)*F_9(x))
Eq(F_21(x, k_0, k_1), (k_0*F_19(x, k_0, k_1) - F_19(x, 1, k_1))/(k_0 - 1))
Eq(F_22(x, k_0, k_1), F_21(x, k_0, k_1)*F_9(x))
Eq(F_23(x, k_0, 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_13(x, k_0/k_1, k_1) + k_1*F_13(x, 1, k_1))/(-k_0 + k_1))
Eq(F_25(x, k_0), k_0*x)
Eq(F_26(x, k_0, k_1), F_13(x, k_0, k_1)*F_25(x, k_1))
Eq(F_27(x), F_5(x)*F_9(x))
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}, {"class_module": "tilings.strategies.sliding", "strategy_class": "SlidingFactory", "use_symmetries": true}], "iterative": false, "name": "row_placements_tracked_fusion_expand_verified", "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, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 3, "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": [[4, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[5, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": 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