01342_01423_01432_02413_10342_10423_10432_12403_20341_20413_20431_21403_30412_30421_31402
Counting sequence:
1, 1, 2, 6, 24, 105, 477, 2224, 10574, 51030, 249180, 1228412, 6104177, 30538331, 153673943, 777280217, 3949337927, 20148036469, 103164447030, 529993224801, 2731044447143, 14112294532210, 73111031365642, 379666192292132, 1975974859406015, 10305190288821134, 53847690193000022, 281878334259847505, 1478059495150114605, 7762723078481689939, 40830844296579989863, 215069175112486157477, 1134357431025512991017, 5990631921344796034396, 31675077641390822199058, 167671232569347548036030, 888526997190301934815510, 4713364332077830776709857, 25027552530047741474461581, 133018743930588682608313666, 707612995699955713997087695, 3767470455101328479914475590, 20075145562923175604421253303, 107055022529254059475876522480, 571321436978450762054802520671, 3051164409539369157357757314692, 16306081119402281561754795390501, 87200806281704538818123068698479, 466623934133089229958938184086001, 2498494835068336662730456779968979, 13385812863140311979619683944810874, 71755690845487294106295184834683927, 384861286537840689138010012007992942, 2065284207652480685740924237438638506, 11088556844747187152327298230585711671, 59563764384952051697151252903257380325, 320106020088705830582558884924956448239, 1721088458945084159660215546546193329406, 9257710155034435836844012513630197852590, 49818278131849129721131315279148012261649, 268196188441927901343314450315384448771917, 1444406835632685174506039162725897810704565, 7782050918936469442175191848132346818386686, 41943146146351696235989858993793620743346146, 226144161073600913274144048266435711540555861, 1219726478534946563798904247493459600224881619, 6580936318022767881486331922649175810721074706, 35518674528161616677413341594229160415890772139, 191763296371360499689320598105315670111322587946, 1035642630322910167134552173700205602035067332022, 5594821522209840950369451220290040210723836360527, 30233664214392660957020507316290947453357127945163, 163425588812441021306753824992204969264405774873619, 883630484974286369362447607123501833339495252811442, 4779026618572982883900180053116746465711857287609660, 25853731234336731808313178782018420193462729041040295, 139900428785814759724559525949548704773853271630484972, 757223398600675495081114946305877738178185716035635403, 4099542622033575192264446720919055067619995530557958724, 22199874903057368962177041186461767337702880542075357742, 120244944636244728104922346858974627201699438739500766712, 651451121041946716536416291278772966553907343785280619366, 3530150121119905000546876520651988789794552351180502778654, 19133681797089699761340459409623765261843254242359377852550, 103727936807670277371254746912362956263835431600386454256088, 562448307770432582298771345773023784018260513827549266826966, 3050402214442465872625941595415400819495926118885158081965706, 16546922209851853731684268345699430058683105415446070319682954, 89776163195838443336847511190437927646313407352137512948711412, 487176904834410807405947923027979858745798989897967645898747256, 2644188287991342994398596022864821614848049733660316589349069110, 14354112788971812704292291989369491284831544901959729680363082330, 77935789114363935174035884244380382880672433787749336952349766004, 423226148978502329935842955090619811990241776509487919598952318438, 2298695471641788165844088871664366541507152089895405372486798595182, 12487118935869216380064927233671366698951004325376853547074023191598, 67844310390150646778797823249255768478083976447762136825452104259780, 368666396447158360384528513540585157772424023417757596431602218788250, 2003647033193077708631327492923110503552889070486752804860312722021312, 10891183375497411902681106996096196017313961375655291625625589620287552, 59209827913469071433944113115540071062624357871871403033512680851443009
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: https://permpal.com/tree/24307/
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[1,x]+F[33,x]+F[5,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[31,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[10,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = F[12,x,1,k[0]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[16,x,k[0],k[1]]+F[18,x,k[0],k[1]]+F[22,x,k[1],k[0]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[3,x]
F[14,x,k[0],k[1]] = 1/(-1+k[0])*(F[15,x,k[0],k[1]]*k[0]-F[15,x,1,k[1]])
F[15,x,k[0],k[1]] = (F[7,x,k[0]]*k[0]-F[7,x,k[1]]*k[1])/(-k[1]+k[0])
F[16,x,k[0],k[1]] = F[17,x,k[0],k[1]]*F[3,x]
F[17,x,k[0],k[1]] = 1/(-1+k[0])*(F[12,x,k[0],k[1]]*k[0]-F[12,x,1,k[1]])
F[18,x,k[0],k[1]] = F[19,x,k[0],k[1]]
F[19,x,k[0],k[1]] = F[12,x,k[0],k[1]]*F[20,x,k[0]]*F[21,x,k[0]]
F[20,x,k[0]] = k[0]*x
F[21,x,k[0]] = F[1,x]+F[20,x,k[0]]
F[22,x,k[0],k[1]] = F[23,x,k[0],k[1]]
F[23,x,k[0],k[1]] = F[20,x,k[0]]*F[24,x,k[1],k[0]]*F[27,x,k[0]]
F[24,x,k[0],k[1]] = F[20,x,k[0]]+F[25,x,k[1]]
F[25,x,k[0]] = F[20,x,k[0]]+F[26,x]
F[26,x] = F[1,x]+F[3,x]
F[27,x,k[0]] = F[1,x]+F[28,x,k[0]]+F[29,x,k[0]]
F[28,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[20,x,k[0]]*F[21,x,k[0]]*F[27,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[20,x,k[0]]*F[25,x,k[0]]*F[27,x,k[0]]
F[33,x] = F[3,x]*F[34,x]
F[34,x] = F[35,x,1]
F[35,x,k[0]] = F[1,x]+F[36,x,k[0]]+F[38,x,k[0]]+F[8,x,k[0]]
F[36,x,k[0]] = F[3,x]*F[37,x,k[0]]
F[37,x,k[0]] = 1/(-1+k[0])*(F[35,x,k[0]]*k[0]-F[35,x,1])
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[20,x,k[0]]*F[21,x,k[0]]*F[35,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_{1}\! \left(x \right)+F_{33}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = \frac{y F_{7}\! \left(x , y\right)-F_{7}\! \left(x , 1\right)}{-1+y}
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , 1, y\right)
F_{12}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y , z\right)+F_{16}\! \left(x , y , z\right)+F_{18}\! \left(x , y , z\right)+F_{22}\! \left(x , z , y\right)
F_{13}\! \left(x , y , z\right) = F_{14}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{14}\! \left(x , y , z\right) = \frac{y F_{15}\! \left(x , y , z\right)-F_{15}\! \left(x , 1, z\right)}{-1+y}
F_{15}\! \left(x , y , z\right) = \frac{y F_{7}\! \left(x , y\right)-z F_{7}\! \left(x , z\right)}{-z +y}
F_{16}\! \left(x , y , z\right) = F_{17}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{17}\! \left(x , y , z\right) = \frac{y F_{12}\! \left(x , y , z\right)-F_{12}\! \left(x , 1, z\right)}{-1+y}
F_{18}\! \left(x , y , z\right) = F_{19}\! \left(x , y , z\right)
F_{19}\! \left(x , y , z\right) = F_{12}\! \left(x , y , z\right) F_{20}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = y x
F_{21}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{20}\! \left(x , y\right)
F_{22}\! \left(x , y , z\right) = F_{23}\! \left(x , y , z\right)
F_{23}\! \left(x , y , z\right) = F_{20}\! \left(x , y\right) F_{24}\! \left(x , z , y\right) F_{27}\! \left(x , y\right)
F_{24}\! \left(x , y , z\right) = F_{20}\! \left(x , y\right)+F_{25}\! \left(x , z\right)
F_{25}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{3}\! \left(x \right)
F_{27}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{25}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{33}\! \left(x \right) = F_{3}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x , 1\right)
F_{35}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{36}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = \frac{y F_{35}\! \left(x , y\right)-F_{35}\! \left(x , 1\right)}{-1+y}
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{35}\! \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_1(x) + F_33(x) + F_5(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_10(x, k_0) + F_31(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_10(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), F_12(x, 1, k_0))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_16(x, k_0, k_1) + F_18(x, k_0, k_1) + F_22(x, k_1, k_0))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_3(x))
Eq(F_14(x, k_0, k_1), (k_0*F_15(x, k_0, k_1) - F_15(x, 1, k_1))/(k_0 - 1))
Eq(F_15(x, k_0, k_1), (-k_0*F_7(x, k_0) + k_1*F_7(x, k_1))/(-k_0 + k_1))
Eq(F_16(x, k_0, k_1), F_17(x, k_0, k_1)*F_3(x))
Eq(F_17(x, k_0, k_1), (k_0*F_12(x, k_0, k_1) - F_12(x, 1, k_1))/(k_0 - 1))
Eq(F_18(x, k_0, k_1), F_19(x, k_0, k_1))
Eq(F_19(x, k_0, k_1), F_12(x, k_0, k_1)*F_20(x, k_0)*F_21(x, k_0))
Eq(F_20(x, k_0), k_0*x)
Eq(F_21(x, k_0), F_1(x) + F_20(x, k_0))
Eq(F_22(x, k_0, k_1), F_23(x, k_0, k_1))
Eq(F_23(x, k_0, k_1), F_20(x, k_0)*F_24(x, k_1, k_0)*F_27(x, k_0))
Eq(F_24(x, k_0, k_1), F_20(x, k_0) + F_25(x, k_1))
Eq(F_25(x, k_0), F_20(x, k_0) + F_26(x))
Eq(F_26(x), F_1(x) + F_3(x))
Eq(F_27(x, k_0), F_1(x) + F_28(x, k_0) + F_29(x, k_0))
Eq(F_28(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_20(x, k_0)*F_21(x, k_0)*F_27(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_20(x, k_0)*F_25(x, k_0)*F_27(x, k_0))
Eq(F_33(x), F_3(x)*F_34(x))
Eq(F_34(x), F_35(x, 1))
Eq(F_35(x, k_0), F_1(x) + F_36(x, k_0) + F_38(x, k_0) + F_8(x, k_0))
Eq(F_36(x, k_0), F_3(x)*F_37(x, k_0))
Eq(F_37(x, k_0), (k_0*F_35(x, k_0) - F_35(x, 1))/(k_0 - 1))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_20(x, k_0)*F_21(x, k_0)*F_35(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:
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