01342_02341_12340
Counting sequence:
1, 1, 2, 6, 24, 117, 652, 3988, 26112, 180126, 1295090, 9631656, 73676572, 577180996, 4615090192, 37562920238, 310523535692, 2602546111313, 22080769557894, 189403492226689, 1640772609911156, 14341379756793722, 126376359608556754, 1121937445109205927, 10028423238950860458, 90203410822880721480, 816077781816532884810, 7422896113445536522770, 67855191206245493953114, 623178219496657692122684, 5748139585358751543320746, 53236243889807422134261397, 494929140699275409898333214, 4617793588333668295222927218, 43230570801633513559114924800, 406002978721999344750543133783, 3824485241352780251504793946878, 36128684528189096268123758715572, 342217388985134858471335363376678, 3249848237238428361217385228830662, 30937124064694994244883316821120734, 295189860722813040075373970699813376, 2822799279869787750459871539290088880, 27050254271261274893580619446990884773, 259737243860713385439283399075568792276, 2498791922227192369835715225195451880368, 24083683773653479938290870721655291640912, 232529979070551724864136870554448883629536, 2248881425802364561211415308602925383417236, 21784922251178639479651657475182086900758731, 211358335868523027440620668153976165677941170, 2053668544232205032249959179736106573644374849, 19983158352094404652399058096962965833850070302, 194714063001290688268294039878851859482097539324, 1899799701025611881654297149865181834179503441362, 18559860784300067195862845960644084616593448070450, 181542465297833665232154296373429684986583254569704, 1777868385538312062069278421825341528050858926390603, 17430950304092619022480720799734200744534464960398892, 171090429502994388508573400382549294097774020522580966, 1681115371479841820363639822211854027207043500151633522, 16535647856676924130528296395202869585078443863223764739, 162810451874463067476654355239666267903216044523827448298, 1604600362424758971566651857547053996056005898707262817269, 15829304758224137416428880947739227127764598476124277401238, 156298411634663017423604261375350205431708574560165851165251, 1544660521309149770451844375126631489687899664877746314310736, 15278679203479173069901713471717416277280926319997636153305435, 151252266166090534727525320861837969162950423400336894698194522, 1498548437480789782314368126903620905429842458631139688807513633, 14858755962773394410401788394125485910180107272236390738290774648, 147444053091505719011454513719732498669473273574399522455098493444, 1464185133470864536702867845151054834569653445621975024153818711066, 14550563086734497270598756434676388259008112656069182283533668429118, 144700553899778394277336188190798411028422801709921166523452039215064, 1439988495364619999700051320200837169786409758743907045735885378539451, 14339646881798978352028111624254398738739801108670091697201608154232690, 142889715412317575165058091226934831507915926830739440208545757239240806, 1424752174674410925575852213138360522034089786118647780350884810807299374, 14214990228687848575589514328654796543191909517120485282855088975544631173, 141910973520168147934461362141598628039053603029577248074168963248932965522, 1417558905980357236163953443218239052748459195947455790234190867114321684423, 14168235017437021226840023459688190595213371953383781582079096021544684098220, 141688269365387924456694647188038148097880720789390515273217431823123751427876, 1417717706009557963899907683800133995631029362795865261058408398483154924285098, 14193116792450197554719299994336826618173276491915096961250676918728041496117852, 142164954596694960487858271119860598523869705673550076272479507133181258379593620, 1424717918744919836593230901919953751895143407981099491300975048174550382245794525, 14285049885155776110415457058842094291410208291270239099554090532661553665627062350, 143300043258705566506745770280608231281585426953006584968885378311240905234664694343, 1438195331341446142850292476011868441853862289847365408383651265964839420072790115354, 14440820928312907396742495454182255519458635107438979399365552965241166884028223233040, 145065438455265062741408180854882658695356615498954995425940286946048399025248902674142, 1457907071753894588017602549370712498477713835648217333136847216009671779164382423461444, 14658361617071502491691306193591279047863440905799563335461386024694716687823733668044262, 147443875342949646538018645530947550302198839084783987167967464242618594112953710464403911, 1483712992394383102853855446911146351038289911383779131279817932382087928879113630290170702, 14936580298212703913060410973668274560776420551977937035773131318485824264512934758001400458, 150427398617379828953041077496866814802388591045984178188638381282377757344291460930259830920, 1515561918534548870904071488622383459680142681525969985119826403353862460611119694038223050715, 15275237915581935613520494706974080075989446766017857937158127037415453896251350746001930565714
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/24020/
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,1,k[0]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[14,x,k[0],k[1]]+F[21,x,k[1],k[0]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[3,x]
F[13,x,k[0],k[1]] = 1/(k[0]*k[1]-1)*(F[11,x,k[0],k[1]]*k[0]*k[1]-F[11,x,1/k[1],k[1]])
F[14,x,k[0],k[1]] = F[15,x,k[0]*k[1],k[1]]
F[16,x,k[0],k[1]] = F[1,x]+F[15,x,k[0],k[1]]+F[17,x,k[0],k[1]]+F[19,x,k[1],k[0]]
F[16,x,k[0],k[1]] = (F[5,x,k[0]]*k[0]-F[5,x,k[1]]*k[1])/(-k[1]+k[0])
F[17,x,k[0],k[1]] = F[18,x,k[0],k[1]]*F[3,x]
F[18,x,k[0],k[1]] = 1/(-1+k[0])*(F[16,x,k[0],k[1]]*k[0]-F[16,x,1,k[1]])
F[19,x,k[0],k[1]] = F[20,x,k[1],k[0]]*F[9,x,k[0]]
F[20,x,k[0],k[1]] = (-F[11,x,1,k[1]]*k[1]+F[11,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[11,x,k[1],k[0]]*F[23,x,k[0]]*F[9,x,k[0]]
F[23,x,k[0]] = F[1,x]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[23,x,k[0]]^2*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_{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\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = \frac{F_{5}\! \left(x , y\right) y -F_{5}\! \left(x , 1\right)}{-1+y}
F_{8}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = y x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , 1, y\right)
F_{11}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{14}\! \left(x , y , z\right)+F_{21}\! \left(x , z , y\right)
F_{12}\! \left(x , y , z\right) = F_{13}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{13}\! \left(x , y , z\right) = \frac{F_{11}\! \left(x , y , z\right) y z -F_{11}\! \left(x , \frac{1}{z}, z\right)}{y z -1}
F_{14}\! \left(x , y , z\right) = F_{15}\! \left(x , y z , z\right)
F_{16}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y , z\right)+F_{17}\! \left(x , y , z\right)+F_{19}\! \left(x , z , y\right)
F_{16}\! \left(x , y , z\right) = \frac{F_{5}\! \left(x , y\right) y -F_{5}\! \left(x , z\right) z}{-z +y}
F_{17}\! \left(x , y , z\right) = F_{18}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{18}\! \left(x , y , z\right) = \frac{F_{16}\! \left(x , y , z\right) y -F_{16}\! \left(x , 1, z\right)}{-1+y}
F_{19}\! \left(x , y , z\right) = F_{20}\! \left(x , z , y\right) F_{9}\! \left(x , y\right)
F_{20}\! \left(x , y , z\right) = \frac{-F_{11}\! \left(x , 1, z\right) z +F_{11}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{21}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = F_{11}\! \left(x , z , y\right) F_{23}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{23}\! \left(x , y\right)^{2} 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_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, 1, k_0))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_14(x, k_0, k_1) + F_21(x, k_1, k_0))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_3(x))
Eq(F_13(x, k_0, k_1), (k_0*k_1*F_11(x, k_0, k_1) - F_11(x, 1/k_1, k_1))/(k_0*k_1 - 1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0*k_1, k_1))
Eq(F_16(x, k_0, k_1), F_1(x) + F_15(x, k_0, k_1) + F_17(x, k_0, k_1) + F_19(x, k_1, k_0))
Eq(F_16(x, k_0, k_1), (-k_0*F_5(x, k_0) + k_1*F_5(x, k_1))/(-k_0 + k_1))
Eq(F_17(x, k_0, k_1), F_18(x, k_0, k_1)*F_3(x))
Eq(F_18(x, k_0, k_1), (k_0*F_16(x, k_0, k_1) - F_16(x, 1, k_1))/(k_0 - 1))
Eq(F_19(x, k_0, k_1), F_20(x, k_1, k_0)*F_9(x, k_0))
Eq(F_20(x, k_0, k_1), (-k_0*F_11(x, k_0/k_1, k_1) + k_1*F_11(x, 1, k_1))/(-k_0 + k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), F_11(x, k_1, k_0)*F_23(x, k_0)*F_9(x, k_0))
Eq(F_23(x, k_0), F_1(x) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_23(x, k_0)**2*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": true, "place_row": false, "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": "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, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 2, "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": [[1, 3]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 4]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 3], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 4], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 3], [1, 3], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 3], [1, 4], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 3], [1, 4], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 4], [1, 4], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 4], [1, 4], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 3], [1, 3], [1, 4], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": 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