01234_01243_02134_02143_02314_20134_20143_20314_23014
Counting sequence:
1, 1, 2, 6, 24, 111, 547, 2788, 14565, 77705, 422154, 2329104, 13017733, 73556463, 419500504, 2411591378, 13959832471, 81300313833, 476030215972, 2800605496679, 16547368872817, 98148095960581, 584188418077005, 3488233997893858, 20889159435741370, 125428086325830452, 754979707197893524, 4554713674405878851, 27535935038325273839, 166796462179800211708, 1012194681376090993324, 6152890514347557329707, 37461483916163732147265, 228422326833467759458691, 1394764591151937047851949, 8527789733164917422241259, 52205073536497294147528849, 319962988164333831054173453, 1963225253575737719037043597, 12058646980815716126445547995, 74141562239130126145199307679, 456286867331056159118504669623, 2810653098295875169350360583875, 17328099978709049926810308173003, 106918224261035581946891147297271, 660227289390081774511350659749159, 4080008488865824380194379392266666, 25231346174201712239563630187674651, 156141494552987809015794939643851142, 966901896999674639008867854303397229, 5991299550425740819326436316356526328, 37146958628929842219952114002266436650, 230451109438132965312639162193283631854, 1430467366525695386013732835163219454485, 8884061588845353080563260666669823591428, 55204054030930409609253530833838890976810, 343200577863762791258352970972090837038358, 2134690574276510219695552888590535336405842, 13283863421631612947364405514070855187961942, 82700752196499298496210103981143508618140423, 515090452606704317706871903022963236242374765, 3209521182111173071437123205011483041908362054, 20006620246893382152413280999482181431322331945, 124760833051554839273223594636828933404006721389, 778302537089083034764490875952138489648453863028, 4857123097497478910139859718151207680551356095882, 30322523165710988264255351661063151285208947645539, 189366183402890150719885648623286896910133605024285, 1183003121005334634110306153014156408884898368002218, 7392842218365806749114766032256602618519968769913854, 46214149146442189976526820126655534032932376351693495, 288983158129119938619373688188875710434214450720706253, 1807591900586935550656066456688079194599005234879070875, 11309799731347248124757761062383646834269185315885839098, 70783601606853147066636749910371115041464153846940764569, 443129121517743181543232148388861788914992158621318500749, 2774882720356550892663156276872260235166253423563841626439, 17380914208016582092567729212804275123019412557513236115380, 108895842301982735312517660008558933260955331974549517320721, 682429590197134842374967189082295382831229621864171710254617, 4277692337416378131528129122276423264886115004213320046130564, 26820308278397435808787637451198216231422388339495996863211541, 168196898675672266748037447704190739133036367742161472603959066, 1055042046990861569607325797425215608143670266031506275142279934, 6619371771032215779843371210221688822169267996266513835829886035, 41539067091428494061236405138080510884420997817307816062492930159, 260727885003664826102528909772794668607229972213425985609294723450, 1636842514932341213151028962641196812584992746094450979605759338550, 10278102641486936371501255142924564584272298001401657766463607365029, 64551104607795227317312012158300899095090132423822724087976599390256, 405487230814094567278136992990455883476737869778378866898163551739899, 2547602271330387923434024315425526048740179191110995530543892429577868, 16009038115994073038287966939185056260638119688838497580423848689118229, 100618143303075399127973628970332595454005325136377161628934568459610027, 632503811534531652739851427708937196102774821350074758750926472230147259, 3976712308247499988523997153411504953074232840314278862524396745556459386, 25006782711241930291988492170485965052613729565970971769977511466333887409, 157276044590116364273236867654105605417993203410297123901492772338893293096, 989320445007704097495431343806810319320845915526183253327414713118927637975, 6224143825595185833098401440378288105782759801784425386326031519241605172371, 39164186439753550013713098918098878052502035917823363568546150162693475902856
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24184/
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[16,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[17,x,k[0]]+F[27,x,k[0]]
F[10,x,k[0]] = F[11,x,1,k[0]]
F[11,x,k[0],k[1]] = F[12,x,k[0]*k[1],k[1]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[7,x]
F[13,x,k[0],k[1]] = 1/(-1+k[0])*(F[14,x,k[0],k[1]]*k[0]-F[14,x,1,k[1]])
F[14,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[15,x,k[0],k[1]]+F[8,x,k[0]]
F[15,x,k[0],k[1]] = F[16,x,k[1]]*F[4,x,k[0]]
F[16,x,k[0]] = k[0]*x
F[17,x,k[0]] = F[18,x,1,k[0]]
F[18,x,k[0],k[1]] = F[19,x,k[0]*k[1],k[1]]
F[19,x,k[0],k[1]] = F[16,x,k[0]]*F[20,x,k[0],k[1]]
F[20,x,k[0],k[1]] = F[1,x]+F[21,x,k[0],k[1]]+F[24,x,k[0],k[1]]+F[27,x,k[0]]+F[33,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[7,x]
F[22,x,k[0],k[1]] = (F[23,x,k[0],1]*k[0]-F[23,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[23,x,k[0],k[1]] = F[13,x,k[0],k[0]*k[1]]
F[24,x,k[0],k[1]] = F[16,x,k[0]]*F[25,x,k[0],k[1]]
F[25,x,k[0],k[1]] = (F[26,x,k[0],1]*k[0]-F[26,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[26,x,k[0],k[1]] = F[20,x,k[0],k[0]*k[1]]
F[27,x,k[0]] = F[16,x,k[0]]*F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0],1]
F[29,x,k[0],k[1]] = F[30,x,k[0],k[0]*k[1]]
F[30,x,k[0],k[1]] = F[1,x]+F[21,x,k[0],k[1]]+F[24,x,k[0],k[1]]+F[31,x,k[0],k[1]]+F[33,x,k[0],k[1]]
F[31,x,k[0],k[1]] = F[16,x,k[0]]*F[32,x,k[0],k[1]]
F[32,x,k[0],k[1]] = (F[29,x,k[0],1]*k[0]-F[29,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[33,x,k[0],k[1]] = F[16,x,k[1]]*F[9,x,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_{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{F_{4}\! \left(x , y\right) y -F_{4}\! \left(x , 1\right)}{-1+y}
F_{7}\! \left(x \right) = x
F_{8}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{17}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , 1, y\right)
F_{11}\! \left(x , y , z\right) = F_{12}\! \left(x , y z , z\right)
F_{12}\! \left(x , y , z\right) = F_{13}\! \left(x , y , z\right) F_{7}\! \left(x \right)
F_{13}\! \left(x , y , z\right) = \frac{F_{14}\! \left(x , y , z\right) y -F_{14}\! \left(x , 1, z\right)}{-1+y}
F_{14}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{15}\! \left(x , y , z\right)+F_{8}\! \left(x , y\right)
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , z\right) F_{4}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = y x
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , 1, y\right)
F_{18}\! \left(x , y , z\right) = F_{19}\! \left(x , y z , z\right)
F_{19}\! \left(x , y , z\right) = F_{16}\! \left(x , y\right) F_{20}\! \left(x , y , z\right)
F_{20}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)+F_{27}\! \left(x , y\right)+F_{33}\! \left(x , y , z\right)
F_{21}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right) F_{7}\! \left(x \right)
F_{22}\! \left(x , y , z\right) = \frac{F_{23}\! \left(x , y , 1\right) y -F_{23}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}
F_{23}\! \left(x , y , z\right) = F_{13}\! \left(x , y , y z \right)
F_{24}\! \left(x , y , z\right) = F_{16}\! \left(x , y\right) F_{25}\! \left(x , y , z\right)
F_{25}\! \left(x , y , z\right) = \frac{F_{26}\! \left(x , y , 1\right) y -F_{26}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}
F_{26}\! \left(x , y , z\right) = F_{20}\! \left(x , y , y z \right)
F_{27}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y , 1\right)
F_{29}\! \left(x , y , z\right) = F_{30}\! \left(x , y , y z \right)
F_{30}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)+F_{31}\! \left(x , y , z\right)+F_{33}\! \left(x , y , z\right)
F_{31}\! \left(x , y , z\right) = F_{16}\! \left(x , y\right) F_{32}\! \left(x , y , z\right)
F_{32}\! \left(x , y , z\right) = \frac{F_{29}\! \left(x , y , 1\right) y -F_{29}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}
F_{33}\! \left(x , y , z\right) = F_{16}\! \left(x , z\right) F_{9}\! \left(x , y\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_16(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_17(x, k_0) + F_27(x, k_0))
Eq(F_10(x, k_0), F_11(x, 1, k_0))
Eq(F_11(x, k_0, k_1), F_12(x, k_0*k_1, k_1))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_7(x))
Eq(F_13(x, k_0, k_1), (k_0*F_14(x, k_0, k_1) - F_14(x, 1, k_1))/(k_0 - 1))
Eq(F_14(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_15(x, k_0, k_1) + F_8(x, k_0))
Eq(F_15(x, k_0, k_1), F_16(x, k_1)*F_4(x, k_0))
Eq(F_16(x, k_0), k_0*x)
Eq(F_17(x, k_0), F_18(x, 1, k_0))
Eq(F_18(x, k_0, k_1), F_19(x, k_0*k_1, k_1))
Eq(F_19(x, k_0, k_1), F_16(x, k_0)*F_20(x, k_0, k_1))
Eq(F_20(x, k_0, k_1), F_1(x) + F_21(x, k_0, k_1) + F_24(x, k_0, k_1) + F_27(x, k_0) + F_33(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1)*F_7(x))
Eq(F_22(x, k_0, k_1), (-k_0*F_23(x, k_0, 1) + k_1*F_23(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_23(x, k_0, k_1), F_13(x, k_0, k_0*k_1))
Eq(F_24(x, k_0, k_1), F_16(x, k_0)*F_25(x, k_0, k_1))
Eq(F_25(x, k_0, k_1), (-k_0*F_26(x, k_0, 1) + k_1*F_26(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_26(x, k_0, k_1), F_20(x, k_0, k_0*k_1))
Eq(F_27(x, k_0), F_16(x, k_0)*F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0, 1))
Eq(F_29(x, k_0, k_1), F_30(x, k_0, k_0*k_1))
Eq(F_30(x, k_0, k_1), F_1(x) + F_21(x, k_0, k_1) + F_24(x, k_0, k_1) + F_31(x, k_0, k_1) + F_33(x, k_0, k_1))
Eq(F_31(x, k_0, k_1), F_16(x, k_0)*F_32(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), (-k_0*F_29(x, k_0, 1) + k_1*F_29(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_33(x, k_0, k_1), F_16(x, k_1)*F_9(x, k_0))
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:
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