01342_03142_03412_03421_10342_13042_30142_30412_30421_31042
Counting sequence:
1, 1, 2, 6, 24, 110, 540, 2762, 14542, 78288, 429076, 2386508, 13437952, 76458612, 438927358, 2539265412, 14789240604, 86647140700, 510317424068, 3019662121676, 17943187032812, 107025169587984, 640566157904136, 3845925145659424, 23156901880100864, 139798049245644094, 846005177745420526, 5131172246637864182, 31186090809063940966, 189907732051457906578, 1158523297527400943632, 7079392335881009565006, 43328120054121479424498, 265573191276515651163030, 1630049487522732868500636, 10018080341739801074335106, 61645780093786553541589298, 379776349207437281378031626, 2342238710341766049613520552, 14460660777527292309048284814, 89366723272199706455025492682, 552806217494452750190378018870, 3422627332098178109207944824536, 21208870539367973766058844804330, 131531445033019644992499145433090, 816356419804917353719354390165306, 5070529405403790453916347310929700, 31516366051509833255102433169833542, 196026709641350335912957933787502586, 1220052176901060073203234811314203234, 7598259071474141424113989447367072838, 47349076563431390293982509532173236790, 295229987546693238103712949935656070410, 1841837707017931854910013056446774464758, 11496751021009708719433480113242497255226, 71799795108947328623399241171424845652602, 448629158889755278166638068049729886380470, 2804531586108351201292266547730875015911740, 17540196428157468235495622934819603076643856, 109749602145118321173954391326684036019897576, 687004047733474145488767233705332797161750892, 4302265977590766415592450208522642231748989328, 26953236302142261868778266551504588555649324842, 168925281744585865056922549651346800433064806240, 1059114929439984769529225488386343242603356168560, 6642799087452934249053538826401697136556448900418, 41678670130761304677861400925560347097001670583692, 261593312447372505015211059048759185155005494820746, 1642422993623898696959814731343512224065087448314406, 10315368175432465121244460898479618967970125083171550, 64806969655515042095019361407860820444441930012565878, 407279039570685927561686862385796216357402157430881666, 2560306940435431661761913389832866871836191477156192686, 16099710030722932614438372987450665721617783215387041044, 101266706784722203490992914175010507035978725434292269880, 637139654175557026949259314830376241417786300927438721600, 4009763283024075495825813953056036807857354317176101014532, 25241545573921336512701086264213133864841572395753765702608, 158936388271072912781984463884582586689796101486353604706210, 1001009297559026170895945592261563146564430873004723899937776, 6306052087258363484305707386071152940114909884792699242216192, 39735534820386160266889506316223287734716129388462366875293246, 250437944552449747421668425021069511683015514067455202565868280, 1578768093064428238859841167719007668936371189063769172581198782, 9954773043208978432451307447514419158284974611390537549902665890, 62782260832780582112272539576169211080179975853471099207886775514, 396034423030320384913952263037594343627381106443783952034676708942, 2498717889336636707856198846942040924960819370959915335915512945774, 15768406233998707278510682746392830639904067123885545275687743867634, 99527410634614763017857186960860101189645001808327994013060775062668, 628318801564514390689338876155848120730581636013166677929774134486116, 3967327260677826945167077742825051713902588319442478828340497773820720, 25055025767587420761090839880664056944747199340642144147245700812265140, 158259150575387903857995009967976536943782367308215888732612053474427664, 999811906503073387140868546017175841009584091884830147924076563587211298, 6317448000705163180752047153524418246610989930560741064575148558739239456, 39924307852583383272573607485308103000741869032335836980231456159837711936, 252350379810513968371166425967297356254963966426589546902080279240233174508, 1595291025383285198098694371698346461075302412391240098259913650606524486294, 10086578272531135075218637173031159588458969112676488878862689062888302215636, 63784391667648043047470799519788943706321904873864964831787398339779911056048
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/24223/
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[34,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[26,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[11,x,k[0]]*F[9,x]
F[11,x,k[0]] = 1/(-1+k[0])*(F[12,x,k[0]]*k[0]-F[12,x,1])
F[12,x,k[0]] = F[1,x]+F[13,x,k[0]]+F[24,x,k[0]]+F[7,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[9,x]
F[14,x,k[0]] = 1/(-1+k[0])*(F[15,x,k[0]]*k[0]-F[15,x,1])
F[15,x,k[0]] = F[16,x,1,k[0]]
F[16,x,k[0],k[1]] = F[17,x,k[0],k[0]*k[1]]
F[17,x,k[0],k[1]] = F[1,x]+F[18,x,k[1]]+F[19,x,k[0],k[1]]+F[21,x,k[0],k[1]]
F[18,x,k[0]] = F[6,x,k[0]]*F[9,x]
F[19,x,k[0],k[1]] = F[17,x,k[0],k[1]]*F[20,x,k[0]]
F[20,x,k[0]] = k[0]*x
F[21,x,k[0],k[1]] = F[20,x,k[1]]*F[22,x,k[0],k[1]]
F[22,x,k[0],k[1]] = (-F[23,x,1,k[1]]*k[1]+F[23,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[23,x,k[0],k[1]] = F[17,x,k[0]*k[1],k[1]]
F[24,x,k[0]] = F[20,x,k[0]]*F[25,x,k[0]]
F[25,x,k[0]] = 1/(-1+k[0])*(F[23,x,1,k[0]]*k[0]-F[23,x,1/k[0],k[0]])
F[26,x,k[0]] = F[20,x,k[0]]*F[27,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0],1]
F[28,x,k[0],k[1]] = F[29,x,k[0],k[0]*k[1]]
F[29,x,k[0],k[1]] = F[1,x]+F[13,x,k[1]]+F[30,x,k[0],k[1]]+F[32,x,k[0],k[1]]+F[7,x,k[1]]
F[30,x,k[0],k[1]] = F[20,x,k[0]]*F[31,x,k[0],k[1]]
F[31,x,k[0],k[1]] = 1/(-1+k[0])*(F[17,x,k[0],k[1]]*k[0]-F[17,x,1,k[1]])
F[31,x,k[0],k[1]] = F[1,x]+F[18,x,k[1]]+F[30,x,k[0],k[1]]+F[32,x,k[0],k[1]]+F[33,x,k[1]]
F[33,x,k[0]] = F[15,x,k[0]]*F[9,x]
F[34,x] = F[35,x]*F[9,x]
F[35,x] = F[12,x,1]
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_{34}\! \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_{26}\! \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_{11}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{11}\! \left(x , y\right) = \frac{F_{12}\! \left(x , y\right) y -F_{12}\! \left(x , 1\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{14}\! \left(x , y\right) = \frac{F_{15}\! \left(x , y\right) y -F_{15}\! \left(x , 1\right)}{-1+y}
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , 1, y\right)
F_{16}\! \left(x , y , z\right) = F_{17}\! \left(x , y , y z \right)
F_{17}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , z\right)+F_{19}\! \left(x , y , z\right)+F_{21}\! \left(x , y , z\right)
F_{18}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{19}\! \left(x , y , z\right) = F_{17}\! \left(x , y , z\right) F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = y x
F_{21}\! \left(x , y , z\right) = F_{20}\! \left(x , z\right) F_{22}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = \frac{-F_{23}\! \left(x , 1, z\right) z +F_{23}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{23}\! \left(x , y , z\right) = F_{17}\! \left(x , y z , z\right)
F_{24}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = \frac{F_{23}\! \left(x , 1, y\right) y -F_{23}\! \left(x , \frac{1}{y}, y\right)}{-1+y}
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_{28}\! \left(x , y , 1\right)
F_{28}\! \left(x , y , z\right) = F_{29}\! \left(x , y , y z \right)
F_{29}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , z\right)+F_{30}\! \left(x , y , z\right)+F_{32}\! \left(x , y , z\right)+F_{7}\! \left(x , z\right)
F_{30}\! \left(x , y , z\right) = F_{20}\! \left(x , y\right) F_{31}\! \left(x , y , z\right)
F_{31}\! \left(x , y , z\right) = \frac{F_{17}\! \left(x , y , z\right) y -F_{17}\! \left(x , 1, z\right)}{-1+y}
F_{31}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , z\right)+F_{30}\! \left(x , y , z\right)+F_{32}\! \left(x , y , z\right)+F_{33}\! \left(x , z\right)
F_{33}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{9}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x , 1\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_34(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_26(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_11(x, k_0)*F_9(x))
Eq(F_11(x, k_0), (k_0*F_12(x, k_0) - F_12(x, 1))/(k_0 - 1))
Eq(F_12(x, k_0), F_1(x) + F_13(x, k_0) + F_24(x, k_0) + F_7(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_9(x))
Eq(F_14(x, k_0), (k_0*F_15(x, k_0) - F_15(x, 1))/(k_0 - 1))
Eq(F_15(x, k_0), F_16(x, 1, k_0))
Eq(F_16(x, k_0, k_1), F_17(x, k_0, k_0*k_1))
Eq(F_17(x, k_0, k_1), F_1(x) + F_18(x, k_1) + F_19(x, k_0, k_1) + F_21(x, k_0, k_1))
Eq(F_18(x, k_0), F_6(x, k_0)*F_9(x))
Eq(F_19(x, k_0, k_1), F_17(x, k_0, k_1)*F_20(x, k_0))
Eq(F_20(x, k_0), k_0*x)
Eq(F_21(x, k_0, k_1), F_20(x, k_1)*F_22(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), (-k_0*F_23(x, k_0/k_1, k_1) + k_1*F_23(x, 1, k_1))/(-k_0 + k_1))
Eq(F_23(x, k_0, k_1), F_17(x, k_0*k_1, k_1))
Eq(F_24(x, k_0), F_20(x, k_0)*F_25(x, k_0))
Eq(F_25(x, k_0), (k_0*F_23(x, 1, k_0) - F_23(x, 1/k_0, k_0))/(k_0 - 1))
Eq(F_26(x, k_0), F_20(x, k_0)*F_27(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0, 1))
Eq(F_28(x, k_0, k_1), F_29(x, k_0, k_0*k_1))
Eq(F_29(x, k_0, k_1), F_1(x) + F_13(x, k_1) + F_30(x, k_0, k_1) + F_32(x, k_0, k_1) + F_7(x, k_1))
Eq(F_30(x, k_0, k_1), F_20(x, k_0)*F_31(x, k_0, k_1))
Eq(F_31(x, k_0, k_1), (k_0*F_17(x, k_0, k_1) - F_17(x, 1, k_1))/(k_0 - 1))
Eq(F_31(x, k_0, k_1), F_1(x) + F_18(x, k_1) + F_30(x, k_0, k_1) + F_32(x, k_0, k_1) + F_33(x, k_1))
Eq(F_33(x, k_0), F_15(x, k_0)*F_9(x))
Eq(F_34(x), F_35(x)*F_9(x))
Eq(F_35(x), F_12(x, 1))
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": [0, 3, 4, 2, 1], "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": [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, 0, 4, 2, 1], "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]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 4, "original_rule": {"children": 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