01243_01342_02143_02341_03142_03241_04132_04231_10243_10342_12043_13042_14032_20143_21043
Counting sequence:
1, 1, 2, 6, 24, 105, 474, 2194, 10392, 50185, 246194, 1223428, 6145544, 31154596, 159187944, 818989246, 4238979424, 22057565033, 115322592658, 605505918134, 3191446966104, 16879741215265, 89560709627850, 476568074070836, 2542638844848216, 13598957356764668, 72896558689311864, 391576904756917152, 2107519024757022304, 11363514525731997704, 61374592639817131088, 332010934731450426046, 1798710869309071658304, 9758358523675222620073, 53010664056864615059730, 288329058381682830324138, 1570082902251324445186808, 8559304016404530881161323, 46710105996719570507473390, 255162320219138311027964186, 1395192102024896086965295176, 7635602352300682632381138625, 41824031252671745235012720162, 229279128169146800850656643660, 1257891306933445864931024489992, 6906319363161957208269727711000, 37945571963463382663856730644080, 208628340281506753415710281476392, 1147812425438845942669902532588608, 6318913002167903444315088638011420, 34807815921603563510641323590936888, 191850907990126853920097007988562440, 1058020214900865119231293780785069984, 5837917735313258375140629544123529836, 32229031620730867952412034117908583480, 178013800402767885919393714976684245376, 983715469713436609951869943844618422560, 5438603923913752582053506088002793475944, 30081572026018641026046699703350318610384, 166457054705298731522185456349716399174400, 921480624447159644649177038273545529585728, 5103246936320610030613987211138327558268880, 28273375991552362825673422062536748728256032, 156701829844948369699076317355079355678828862, 868821655897923520721968115583296728079716096, 4818839593904180530779676161027361467751167529, 26736520080274274174544169441342180307071883026, 148392992401905201696603033799416860980923729234, 823879556802083637046841127914126427878446891064, 4575639373529286567185317157462186092805734327935, 25419889502627076324501059963104408802606039945014, 141262075208537537369055642270816946028870462532262, 785242795397753515222260663678483247163054791491880, 4366217263339933277774972307749421731671289792733595, 24284346221774061502982691053314251471109737795984406, 135102691492521387231007407537032070471244939164171260, 751822022015913981632151785829614961199548180391644056, 4184818285174849609409097769882568746234869518829448484, 23299460390815005051764338271048851776556277922960052712, 129753804573377043645873404161973118207430130018788511630, 722764316301255250442119664902872650256158587445266378592, 4026921372953712255597799263158204355916787803144969397729, 22441248518666773032622759714622976860567791089845977624194, 125088089375511233554573748049185041291824181099395231677526, 697393226768628317941793766406502779821094589975488528614680, 3888930093176416044118512049128220314795024625102751989913281, 21690576335679387565041909618884751609244569485185205915098890, 121003675425881713171235879901166334603821742903963945827715500, 675166036058865931163240507192785802280241160696859760198135640, 3767951230863787966142871910382150446043835331295671930172354640, 21032010421167793949974651991431516919376287137909192845859978144, 117418184710817153086080228091099760591635549259177089632197171968, 655642775826740352303072798282167369416711157428547227944872902272, 3661633604723470136723562536995511784727309693807575862229237178528, 20452978926063187183913230156638578981639246680354199010121006454336, 114264357591207080680000172834278077279471076479095752545915290895496, 638463409676375325144097489933987744214844493907328702574640398959872, 3568048939093471106023434271675740779662898165474729636630415059756444, 19943149070256334482344082619102989358292979326182971001221588727815224, 111486797190133030799358245269218313416958538281632841556778499835703960, 623330792743097963941382132635950045316408112249468031741432011209144352
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: https://permpal.com/tree/24296/
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[43,x]+F[5,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[1,x]+F[41,x]+F[42,x]+F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[12,x,k[0]]+F[37,x,k[0]]+F[40,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[12,x,k[0]] = F[13,x,k[0]]*F[3,x]
F[13,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[31,x,k[0]]+F[33,x,k[0]]+F[36,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[3,x]
F[16,x,k[0]] = 1/(-1+k[0])*(F[17,x,k[0]]*k[0]-F[17,x,1])
F[17,x,k[0]] = 1/(-1+k[0])*(F[18,x,k[0]]*k[0]-F[18,x,1])
F[18,x,k[0]] = F[1,x]+F[19,x,k[0]]+F[20,x,k[0]]+F[8,x,k[0]]
F[19,x,k[0]] = F[14,x,k[0]]*F[3,x]
F[20,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = F[1,x]+F[23,x,k[0]]+F[24,x,k[0]]+F[30,x,k[0]]
F[23,x,k[0]] = F[17,x,k[0]]*F[3,x]
F[24,x,k[0]] = F[25,x,k[0]]*F[3,x]
F[25,x,k[0]] = 1/(-1+k[0])*(F[26,x,k[0]]*k[0]-F[26,x,1])
F[26,x,k[0]] = F[1,x]+F[23,x,k[0]]+F[24,x,k[0]]+F[27,x,k[0]]
F[27,x,k[0]] = F[21,x,k[0]]*F[28,x,k[0]]
F[28,x,k[0]] = F[1,x]+F[27,x,k[0]]+F[29,x,k[0]]
F[29,x,k[0]] = F[18,x,k[0]]*F[3,x]
F[30,x,k[0]] = F[21,x,k[0]]*F[26,x,k[0]]
F[31,x,k[0]] = F[3,x]*F[32,x,k[0]]
F[32,x,k[0]] = 1/(-1+k[0])*(F[25,x,k[0]]*k[0]-F[25,x,1])
F[33,x,k[0]] = F[3,x]*F[34,x,k[0]]
F[34,x,k[0]] = 1/(-1+k[0])*(F[35,x,k[0]]*k[0]-F[35,x,1])
F[35,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[27,x,k[0]]+F[31,x,k[0]]+F[33,x,k[0]]
F[36,x,k[0]] = F[21,x,k[0]]*F[35,x,k[0]]
F[37,x,k[0]] = F[3,x]*F[38,x,k[0]]
F[38,x,k[0]] = 1/(-1+k[0])*(F[39,x,k[0]]*k[0]-F[39,x,1])
F[39,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[30,x,k[0]]+F[31,x,k[0]]+F[33,x,k[0]]
F[40,x,k[0]] = F[21,x,k[0]]*F[39,x,k[0]]
F[41,x] = F[19,x,1]
F[42,x] = F[40,x,1]
F[43,x] = F[3,x]*F[44,x]
F[44,x] = F[1,x]+F[45,x]+F[48,x]+F[51,x]
F[45,x] = F[3,x]*F[46,x]
F[46,x] = F[47,x,1]
F[47,x,k[0]] = 1/(-1+k[0])*(F[18,x,k[0]]*k[0]-F[18,x,1])
F[48,x] = F[3,x]*F[49,x]
F[49,x] = F[50,x,1]
F[50,x,k[0]] = 1/(-1+k[0])*(F[26,x,k[0]]*k[0]-F[26,x,1])
F[51,x] = F[36,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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{43}\! \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_{1}\! \left(x \right)+F_{41}\! \left(x \right)+F_{42}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{3}\! \left(x \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_{12}\! \left(x , y\right)+F_{37}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{13}\! \left(x , y\right) = -\frac{-y F_{14}\! \left(x , y\right)+F_{14}\! \left(x , 1\right)}{-1+y}
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{33}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{16}\! \left(x , y\right) = -\frac{-y F_{17}\! \left(x , y\right)+F_{17}\! \left(x , 1\right)}{-1+y}
F_{17}\! \left(x , y\right) = -\frac{-y F_{18}\! \left(x , y\right)+F_{18}\! \left(x , 1\right)}{-1+y}
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{20}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{23}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{25}\! \left(x , y\right) = -\frac{-y F_{26}\! \left(x , y\right)+F_{26}\! \left(x , 1\right)}{-1+y}
F_{26}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{23}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{30}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = -\frac{-y F_{25}\! \left(x , y\right)+F_{25}\! \left(x , 1\right)}{-1+y}
F_{33}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = -\frac{-y F_{35}\! \left(x , y\right)+F_{35}\! \left(x , 1\right)}{-1+y}
F_{35}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = -\frac{-y F_{39}\! \left(x , y\right)+F_{39}\! \left(x , 1\right)}{-1+y}
F_{39}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{30}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{41}\! \left(x \right) = F_{19}\! \left(x , 1\right)
F_{42}\! \left(x \right) = F_{40}\! \left(x , 1\right)
F_{43}\! \left(x \right) = F_{3}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{1}\! \left(x \right)+F_{45}\! \left(x \right)+F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{45}\! \left(x \right) = F_{3}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x , 1\right)
F_{47}\! \left(x , y\right) = -\frac{-y F_{18}\! \left(x , y\right)+F_{18}\! \left(x , 1\right)}{-1+y}
F_{48}\! \left(x \right) = F_{3}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x , 1\right)
F_{50}\! \left(x , y\right) = -\frac{-y F_{26}\! \left(x , y\right)+F_{26}\! \left(x , 1\right)}{-1+y}
F_{51}\! \left(x \right) = F_{36}\! \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_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_43(x) + F_5(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_1(x) + F_41(x) + F_42(x) + F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_12(x, k_0) + F_37(x, k_0) + F_40(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_12(x, k_0), F_13(x, k_0)*F_3(x))
Eq(F_13(x, k_0), (k_0*F_14(x, k_0) - F_14(x, 1))/(k_0 - 1))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0) + F_31(x, k_0) + F_33(x, k_0) + F_36(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_3(x))
Eq(F_16(x, k_0), (k_0*F_17(x, k_0) - F_17(x, 1))/(k_0 - 1))
Eq(F_17(x, k_0), (k_0*F_18(x, k_0) - F_18(x, 1))/(k_0 - 1))
Eq(F_18(x, k_0), F_1(x) + F_19(x, k_0) + F_20(x, k_0) + F_8(x, k_0))
Eq(F_19(x, k_0), F_14(x, k_0)*F_3(x))
Eq(F_20(x, k_0), F_21(x, k_0)*F_22(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), F_1(x) + F_23(x, k_0) + F_24(x, k_0) + F_30(x, k_0))
Eq(F_23(x, k_0), F_17(x, k_0)*F_3(x))
Eq(F_24(x, k_0), F_25(x, k_0)*F_3(x))
Eq(F_25(x, k_0), (k_0*F_26(x, k_0) - F_26(x, 1))/(k_0 - 1))
Eq(F_26(x, k_0), F_1(x) + F_23(x, k_0) + F_24(x, k_0) + F_27(x, k_0))
Eq(F_27(x, k_0), F_21(x, k_0)*F_28(x, k_0))
Eq(F_28(x, k_0), F_1(x) + F_27(x, k_0) + F_29(x, k_0))
Eq(F_29(x, k_0), F_18(x, k_0)*F_3(x))
Eq(F_30(x, k_0), F_21(x, k_0)*F_26(x, k_0))
Eq(F_31(x, k_0), F_3(x)*F_32(x, k_0))
Eq(F_32(x, k_0), (k_0*F_25(x, k_0) - F_25(x, 1))/(k_0 - 1))
Eq(F_33(x, k_0), F_3(x)*F_34(x, k_0))
Eq(F_34(x, k_0), (k_0*F_35(x, k_0) - F_35(x, 1))/(k_0 - 1))
Eq(F_35(x, k_0), F_1(x) + F_15(x, k_0) + F_27(x, k_0) + F_31(x, k_0) + F_33(x, k_0))
Eq(F_36(x, k_0), F_21(x, k_0)*F_35(x, k_0))
Eq(F_37(x, k_0), F_3(x)*F_38(x, k_0))
Eq(F_38(x, k_0), (k_0*F_39(x, k_0) - F_39(x, 1))/(k_0 - 1))
Eq(F_39(x, k_0), F_1(x) + F_15(x, k_0) + F_30(x, k_0) + F_31(x, k_0) + F_33(x, k_0))
Eq(F_40(x, k_0), F_21(x, k_0)*F_39(x, k_0))
Eq(F_41(x), F_19(x, 1))
Eq(F_42(x), F_40(x, 1))
Eq(F_43(x), F_3(x)*F_44(x))
Eq(F_44(x), F_1(x) + F_45(x) + F_48(x) + F_51(x))
Eq(F_45(x), F_3(x)*F_46(x))
Eq(F_46(x), F_47(x, 1))
Eq(F_47(x, k_0), (-k_0*F_18(x, k_0) + F_18(x, 1))/(1 - k_0))
Eq(F_48(x), F_3(x)*F_49(x))
Eq(F_49(x), F_50(x, 1))
Eq(F_50(x, k_0), (-k_0*F_26(x, k_0) + F_26(x, 1))/(1 - k_0))
Eq(F_51(x), F_36(x, 1))
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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