02341_02431_03241_03412_03421_04231_04312_04321_20341_20431
Counting sequence:
1, 1, 2, 6, 24, 110, 544, 2826, 15200, 83910, 472688, 2706298, 15701616, 92114062, 545487968, 3256445290, 19576659648, 118411209782, 720105016144, 4400362978106, 27005508979024, 166380171930846, 1028671368851392, 6380280732357386, 39689079680972704, 247551373276859046, 1547854831826465840, 9700269791811199482, 60919071179555469104, 383330649844176996526, 2416497037683442494240, 15259450113325220467242, 96512575046304738120064, 611333598813629985996566, 3877776789444883642481424, 24629852179650666817366714, 156632755043389327574426640, 997275589513795314134600446, 6356705157880577834385222272, 40560924655789091684019927498, 259071173400850339585468409952, 1656319523737053880026764710022, 10598949711705373282188163914736, 67882300484604475757443799354490, 435118859984246860742697060965360, 2791262662761709995231653734051534, 17919250015098038659289984456690144, 115120095286695448475448993547697386, 740084663215299523227726684791453760, 4761000302856382087407244475128317430, 30647136310506844687283582672744518352, 197399259651177735592075934679791476282, 1272198129334407810957322238425971272400, 8203664245610034582950092035278378594078, 52929247651019486859371413260067335038272, 341672179038985132267907481311872714067594, 2206690234886708777048214678173657612827936, 14258808347200304906111320609467342085080678, 92178119438715684468947285772434028456074160, 596167420273347619445818266209418386939082490, 3857427746286551184940226297414466068938644656, 24969522681945588156794285381907101379211159278, 161696113484036751929031313758604382706710796448, 1047514715301537625283076123930724207582606098858, 6788697764106878608785402991839723837199240721152, 44012236645400468088204851514412684824364033374422, 285440832738327011844388601760494110766619430531728, 1851866816549393169185803858278693650743642361941434, 12018489659954612752730111369666534339117953992998288, 78024723051813949646114673225238213920250314396873022, 506702052689391823253688333938029372661537823952994304, 3291601430898282836480564064536321824182470192693209418, 21389084825766688884901435819604712720993248494591661536, 139028530405779690562119530955112083280786331612114609222, 903938670060216873713785419084593273097121702745144660848, 5878871657839744588155521167373979376335058687672158886266, 38244217615706947649065935067004778294436109143896969353584, 248857826833005076353430151289344672921730494712609514539278, 1619748561701721179262935302500919294876040036232215202264928, 10545127690109245107097343875765037344934107868269862898907242, 68669090884377261768044539506613243760609933433367229224001984, 447273680356158331600056279993368402928893694794150989822103478, 2913972516184190455545310279603649005306689004848903058883394128, 18988697998366344268653147361126415596885069088171372545187361082, 123765671937899283636572956008346993376458677376591505418818649168, 806860095758902597650449692503702597393137803126740952357106329950, 5261227769775268973805216710365256745549261380843195794732943760064, 34313474427894345458440739519380514257730316583524320726990528061962, 223835504967190039634576953086197913324387274905490295830606466372256, 1460420700059945750367950899328100331137951837617377390549953988092454, 9530371009379091258084273416724540998179163580337910039444826114171696, 62204617222584840296898526903294113548971383109882767635203920305449978, 406082848269239556420630134917901694686709138279139704532458348390298160, 2651454402574453435267221518891923911997075896193440271636786162665401646, 17315279560226471806465664561886151149280222219729470099429395645051192864, 113096475493693790432817386066483294374016044409077978924525505149613586730, 738824507362901931892018291902926563872492874457296387278612172835148702848, 4827304149118067175549731055033182357132602029101750971120552002072837898902, 31545521875637782549353246513472122294857466517657467571482250452034330987024, 206176439130876415364035305278561053608260937107629949804196444333759541330106, 1347743483228258913641931715509313792995114255694692107277897787445943678551824
Specification 1
Strategy pack name: row_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/24234/
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[18,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,1,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[12,x,k[0],k[1]]+F[4,x,k[1]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[18,x,k[0]]
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1]]+F[20,x,k[0],k[1]]
F[15,x,k[0],k[1]] = F[16,x,k[1]]*F[19,x,k[0]]
F[17,x,k[0]] = F[16,x,k[0]]*F[18,x,k[0]]
F[4,x,k[0]] = F[0,x]+F[17,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0]] = F[1,x]+F[18,x,k[0]]
F[20,x,k[0],k[1]] = F[16,x,k[1]]*F[18,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_{18}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , 1, y\right)
F_{10}\! \left(x , y , z\right) = F_{11}\! \left(x , y z , z\right)
F_{11}\! \left(x , y , z\right) = F_{12}\! \left(x , y , z\right)+F_{4}\! \left(x , z\right)
F_{12}\! \left(x , y , z\right) = F_{13}\! \left(x , y , z\right)
F_{13}\! \left(x , y , z\right) = F_{14}\! \left(x , y , z\right) F_{18}\! \left(x , y\right)
F_{14}\! \left(x , y , z\right) = F_{15}\! \left(x , y , z\right)+F_{20}\! \left(x , y , z\right)
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , z\right) F_{19}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{4}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{17}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)
F_{20}\! \left(x , y , z\right) = F_{16}\! \left(x , z\right) F_{18}\! \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_18(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, 1, k_0))
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_12(x, k_0, k_1) + F_4(x, 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_14(x, k_0, k_1)*F_18(x, k_0))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1) + F_20(x, k_0, k_1))
Eq(F_15(x, k_0, k_1), F_16(x, k_1)*F_19(x, k_0))
Eq(F_17(x, k_0), F_16(x, k_0)*F_18(x, k_0))
Eq(F_4(x, k_0), F_0(x) + F_17(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0), F_1(x) + F_18(x, k_0))
Eq(F_20(x, k_0, k_1), F_16(x, k_1)*F_18(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": 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, 3, 4, 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], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "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": [0, 3, 4, 2, 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], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "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": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[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": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 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], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "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": [0, 3, 4, 2, 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], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "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": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [2, 2], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 2], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[2, 2], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 2], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 2], [2, 2], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [2, 2], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 2], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], 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