01342_03142_03412_10342_13042_13402_30142_30412_31042_31402_34012_34102
Counting sequence:
1, 1, 2, 6, 24, 108, 512, 2506, 12560, 64148, 332704, 1747748, 9280416, 49731768, 268613568, 1460847018, 7992819600, 43965495588, 242989734432, 1348696517964, 7514649244128, 42016005233352, 235665924826176, 1325673785058180, 7477059086539424, 42275419332388168, 239567065205029952, 1360430550201086216, 7740541529962849600, 44121903718663304816, 251926012956167788416, 1440723346709420323050, 8251526397226054378896, 47325506341456085391044, 271786623474630428921632, 1562788803506076123276092, 8996677655300269717462880, 51849710099274003611880232, 299135253656989772968570688, 1727518371379928454124795692, 9985964362150530485633093856, 57776286878192693593012410072, 334566888415810890109628624064, 1938977296357297668690780126072, 11246122791729048828273340522176, 65276702838022040177312854687248, 379162018386459854897967213964416, 2203887896727351931462092857872452, 12818578802907040062728896459099296, 74604385827938481830036016591676968, 434462240601801508475329890307377984, 2531585750986910546600168334851175288, 14759664794912254679344147270042228416, 86098276565704160505129878429889486288, 502502127052964432971614450309457836672, 2934260529558409958200729899476504572104, 17142297742809733369814446663673080838976, 100193989631846794863438089051656145000208, 585881298957241605707816302422627915922560, 3427412198959300374395229820786600381361424, 20058826079181414729753761725433868754829952, 117441395210113950495431812877518683380531424, 687872163841724453951139456406351988547211008, 4030507285692431229515124627225048578233718634, 23625008778897280982203179989975157970298999184, 138528657830353603112437099415657127651658695684, 812564723246756738736447014995906058542838925600, 4767849187430588997060167064242521466517468492444, 27985236389160897737863521028316080227410024056416, 164313510870831784437152863574548534884231700590312, 965053683684004124265974996517414356176349874494784, 5669696529192648956770750786472761652195311574048796, 33319210031880638533346118531197139691350794765717088, 195863118372582883099492463436163691613210954486406200, 1151676232712791061247592012442399710904386521245396928, 6773680872226457523721023267251852796666142168213246488, 39850391241666605844724772639656670444790011733840246720, 234504422853756838917247747013666828721095231919952413648, 1380311960252026234533905517248856496072783427694817258112, 8126592987747720439234773223955537594539386154771072879852, 47856638959472017530990431480339382696406105977645766642400, 281887478810888775481208067097163656208822685984896167665464, 1660759912179625919782323379294456881712523319721615284746176, 9786627447438641209074951322774802915192612274435322325567336, 57683570672143779423382512641302661677397642084593499454417984, 340064982333224833479996003127128079800709441144935651792656496, 2005211958269693399853156628133485927467451178551251126985140096, 11826200085609889873780660499839146735994771144737530364027183800, 69761331545278897919058782352151346381868238971868725790142673088, 411592077809463680288535127338566893823404742420916427669783530224, 2428846822056866792706535049244189739654069228558939325773621531520, 14335483562801876293914111020224695847541584418479628599704196471408, 84625637675796166669772601999607632349398732803958861799548809996672, 499651606454183581127269015671181972775669113720617756349050932170272, 2950575566619383450873896792722924871437695755786574863788787290761472, 17426844619940691203062420740910668586130860741147730301770153055364548, 102944187920369954062827878916073761421914578758564675417624856213823648, 608211320850328169365686702434380699182156515406286277494091470148815080, 3593977426329137610994692434217117322949885631731520586787962875498041664, 21240414835820696095710002540784456876372219653125555025000684553687707544, 125549826043436215314932204120654409881660015237404901275197222335558351808
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/24264/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[14,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[41,x]
F[4,x] = F[14,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[38,x,k[0]]+F[39,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[14,x]*F[8,x,k[0]]
F[8,x,k[0]] = F[1,x]+F[31,x,k[0]]+F[33,x,k[0]]+F[34,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[14,x]
F[10,x,k[0]] = 1/(-1+k[0])*(F[11,x,k[0]]*k[0]-F[11,x,1])
F[11,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[23,x,k[0]]+F[25,x,k[0]]+F[26,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x]*F[15,x,k[0]]*F[5,x]
F[14,x] = x
F[15,x,k[0]] = 1/(-1+k[0])*(F[16,x,k[0]]*k[0]-F[16,x,1])
F[16,x,k[0]] = F[1,x]+F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[20,x,k[0]]
F[18,x,k[0]] = F[1,x]+F[19,x,k[0]]+F[21,x,k[0]]
F[19,x,k[0]] = F[18,x,k[0]]*F[20,x,k[0]]
F[20,x,k[0]] = k[0]*x
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[16,x,k[0]]*F[18,x,k[0]]*F[20,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[14,x]*F[15,x,k[0]]*F[5,x]
F[25,x,k[0]] = F[10,x,k[0]]*F[14,x]
F[26,x,k[0]] = F[20,x,k[0]]*F[27,x,k[0]]
F[27,x,k[0]] = F[1,x]+F[19,x,k[0]]+F[28,x,k[0]]+F[29,x,k[0]]
F[28,x,k[0]] = F[14,x]*F[27,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[16,x,k[0]]*F[20,x,k[0]]*F[27,x,k[0]]
F[31,x,k[0]] = F[14,x]*F[32,x,k[0]]
F[32,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[33,x,k[0]] = F[14,x]*F[32,x,k[0]]
F[6,x,k[0]] = F[1,x]+F[34,x,k[0]]+F[35,x,k[0]]+F[37,x,k[0]]
F[35,x,k[0]] = F[14,x]*F[36,x,k[0]]
F[36,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[37,x,k[0]] = F[14,x]*F[36,x,k[0]]
F[38,x,k[0]] = F[11,x,k[0]]*F[14,x]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[16,x,k[0]]*F[20,x,k[0]]*F[6,x,k[0]]
F[41,x] = F[14,x]*F[5,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_{14}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{41}\! \left(x \right)
F_{4}\! \left(x \right) = F_{14}\! \left(x \right) F_{5}\! \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_{38}\! \left(x , y\right)+F_{39}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{31}\! \left(x , y\right)+F_{33}\! \left(x , y\right)+F_{34}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{10}\! \left(x , y\right) = -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{23}\! \left(x , y\right)+F_{25}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{15}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x , y\right) = -\frac{-y F_{16}\! \left(x , y\right)+F_{16}\! \left(x , 1\right)}{-1+y}
F_{16}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = y x
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{15}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{25}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{28}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{27}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{20}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{33}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{37}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{20}\! \left(x , y\right) F_{6}\! \left(x , y\right)
F_{41}\! \left(x \right) = F_{14}\! \left(x \right) F_{5}\! \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_14(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_41(x))
Eq(F_4(x), F_14(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_38(x, k_0) + F_39(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_14(x)*F_8(x, k_0))
Eq(F_8(x, k_0), F_1(x) + F_31(x, k_0) + F_33(x, k_0) + F_34(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_14(x))
Eq(F_10(x, k_0), (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_11(x, k_0), F_1(x) + F_12(x, k_0) + F_23(x, k_0) + F_25(x, k_0) + F_26(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x)*F_15(x, k_0)*F_5(x))
Eq(F_14(x), x)
Eq(F_15(x, k_0), (k_0*F_16(x, k_0) - F_16(x, 1))/(k_0 - 1))
Eq(F_16(x, k_0), F_1(x) + F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_20(x, k_0))
Eq(F_18(x, k_0), F_1(x) + F_19(x, k_0) + F_21(x, k_0))
Eq(F_19(x, k_0), F_18(x, k_0)*F_20(x, k_0))
Eq(F_20(x, k_0), k_0*x)
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_16(x, k_0)*F_18(x, k_0)*F_20(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_14(x)*F_15(x, k_0)*F_5(x))
Eq(F_25(x, k_0), F_10(x, k_0)*F_14(x))
Eq(F_26(x, k_0), F_20(x, k_0)*F_27(x, k_0))
Eq(F_27(x, k_0), F_1(x) + F_19(x, k_0) + F_28(x, k_0) + F_29(x, k_0))
Eq(F_28(x, k_0), F_14(x)*F_27(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_16(x, k_0)*F_20(x, k_0)*F_27(x, k_0))
Eq(F_31(x, k_0), F_14(x)*F_32(x, k_0))
Eq(F_32(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_33(x, k_0), F_14(x)*F_32(x, k_0))
Eq(F_6(x, k_0), F_1(x) + F_34(x, k_0) + F_35(x, k_0) + F_37(x, k_0))
Eq(F_35(x, k_0), F_14(x)*F_36(x, k_0))
Eq(F_36(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_37(x, k_0), F_14(x)*F_36(x, k_0))
Eq(F_38(x, k_0), F_11(x, k_0)*F_14(x))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_16(x, k_0)*F_20(x, k_0)*F_6(x, k_0))
Eq(F_41(x), F_14(x)*F_5(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}], "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, 1, 3, 4, 2], "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, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 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, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], 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