01342_03142_03412_03421_10342_13042_13402_30142_30412_30421_31042_31402_34012_34021_34102
Counting sequence:
1, 1, 2, 6, 24, 105, 477, 2218, 10504, 50516, 246167, 1213329, 6039842, 30326676, 153431887, 781462780, 4003797928, 20621757297, 106715690911, 554591870462, 2893232259271, 15146191513326, 79542577273547, 418942551686626, 2212404998141439, 11712212487159940, 62143616211139217, 330419226774741183, 1760276370830129529, 9394751578542792289, 50225756924213205235, 268941163986095376039, 1442231250931894528256, 7744982539252734194588, 41646489372997644955783, 224220998538330646682425, 1208604756788455239814838, 6521913761803919554990602, 35230863889217186714519741, 190504703771570080871822516, 1031099805012129039578859185, 5585837365795078434994470371, 30286553922508832117407207909, 164349402035973625594962738487, 892538508140647314610845967902, 4850776974838759964299559479735, 26381961551177247908156650942732, 143582365482528406414906992340838, 781953638035992822207237851188014, 4261231931272635784933360488282816, 23235535704953424032842957097281167, 126771980822543369323380406714103784, 692049633721612291273640737879765972, 3779944708829582460457092208339679246, 20656619568733413011008256455754761272, 112940703029737643899762995864261825325, 617805003694849131374181613369271076873, 3381074402436687340845104738545502361802, 18512004879343340735248739989002813884201, 101400712935233407724384766773598423502380, 555662534737663258625745726441423312444779, 3046195804043487853846642857222124851001681, 16706113720491100414918279773602065674428386, 91655506884465216570890715349820229903389618, 503039459036034955346939557913454768545833080, 2761855709715426927733757881702083074118933025, 15168780531653773260580353128125911343441205647, 83338679671907980055657474277529969301418942198, 458020105265044452490428933879333825476749583619, 2518026789420944047100536094163000228478472900346, 13847459442700298920241929594398369343270018762647, 76174576467609296115911924455781434550268895485874, 419156862541527373863988646268832151588156139614977, 2307099064773296784936330610199954920525949598324726, 12702105562663968208451094120614091320196541105260887, 69952271202910021549610056934708491584175583478670235, 385337690008322841644126972389122089426440454247402933, 2123204307707307097469785156768469003789929533645436767, 11701724873605772177642854783346250369397865519804358921, 64507922800431396543661106819351047173565084238551124451, 355695762463409113549621049959781933698538821320056407055, 1961752712569569942608384024413996252906898076792877499486, 10821995240184225758890859682684390793754596494075196533989, 59712544623966042181788579669966598762704946064610865749072, 329546514937544765355487320710135186867457754763495450712797, 1819108452253178449534391588529732537448999865216448351968925, 10043592425742991807332190451000099598233774961587012331644512, 55463357689551739386166585003897870393422786298284221033389798, 306342929323761815178710317335891778666962815630865243768601459, 1692358212550640144208498744376476278917300497806872702836716674, 9350990619642292125321441605777522529337128212418851846236429580, 51677568559712106688335682865623598447125180110326581449109314154, 285643225890720156589049158140716444171765166812517557286944634961, 1579143266355466391644615198482584069234678298896843279018338750373, 8731588803153556789201142573320497914479435379919603360569365738378, 48287820057533282638889023584906763428993073702734180445208264154315, 267087152336934544728115462699983837774789141768047246878867758418543, 1477535782877789344685200071401849728311279136572796587989834879041612, 8175064946868020245661915177556622545309251816561845664363097046163061, 45238816625085686251193797238994370858446402453259905899994933764112667, 250378335091608608381938972702858954836000155844655441006075895437326231
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/24310/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[14,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[51,x]
F[4,x] = F[14,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[48,x,k[0]]+F[49,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[14,x]*F[8,x,k[0]]
F[8,x,k[0]] = F[1,x]+F[37,x,k[0]]+F[39,x,k[0]]+F[42,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[14,x]
F[10,x,k[0]] = 1/(-1+k[0])*(F[11,x,k[0]]*k[0]-F[11,x,1])
F[11,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[20,x,k[0]]+F[29,x,k[0]]+F[33,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x]*F[15,x,k[0]]*F[5,x]
F[14,x] = x
F[15,x,k[0]] = 1/(-1+k[0])*(F[16,x,k[0]]*k[0]-F[16,x,1])
F[16,x,k[0]] = F[1,x]+F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[16,x,k[0]]^2*F[19,x,k[0]]
F[19,x,k[0]] = k[0]*x
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[14,x]*F[15,x,k[0]]*F[22,x]
F[22,x] = F[23,x,1]
F[23,x,k[0]] = 1/(-1+k[0])*(F[24,x,k[0]]*k[0]-F[24,x,1])
F[24,x,k[0]] = F[1,x]+F[25,x,k[0]]+F[31,x,k[0]]
F[25,x,k[0]] = F[14,x]*F[26,x,k[0]]
F[26,x,k[0]] = F[1,x]+F[27,x,k[0]]+F[28,x,k[0]]+F[29,x,k[0]]
F[27,x,k[0]] = F[11,x,k[0]]*F[14,x]
F[28,x,k[0]] = F[14,x]*F[8,x,k[0]]
F[24,x,k[0]] = F[1,x]+F[29,x,k[0]]+F[30,x,k[0]]
F[30,x,k[0]] = F[14,x]*F[6,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[16,x,k[0]]*F[19,x,k[0]]*F[24,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[14,x]*F[35,x]*F[36,x,k[0]]
F[35,x] = F[24,x,1]
F[36,x,k[0]] = 1/(-1+k[0])*(F[15,x,k[0]]*k[0]-F[15,x,1])
F[37,x,k[0]] = F[14,x]*F[38,x,k[0]]
F[38,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[39,x,k[0]] = F[14,x]*F[40,x,k[0]]
F[40,x,k[0]] = 1/(-1+k[0])*(F[41,x,k[0]]*k[0]-F[41,x,1])
F[41,x,k[0]] = 1/(-1+k[0])*(F[26,x,k[0]]*k[0]-F[26,x,1])
F[6,x,k[0]] = F[1,x]+F[42,x,k[0]]+F[43,x,k[0]]+F[45,x,k[0]]
F[43,x,k[0]] = F[14,x]*F[44,x,k[0]]
F[44,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[45,x,k[0]] = F[14,x]*F[46,x,k[0]]
F[46,x,k[0]] = 1/(-1+k[0])*(F[47,x,k[0]]*k[0]-F[47,x,1])
F[47,x,k[0]] = 1/(-1+k[0])*(F[24,x,k[0]]*k[0]-F[24,x,1])
F[48,x,k[0]] = F[11,x,k[0]]*F[14,x]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[16,x,k[0]]*F[19,x,k[0]]*F[6,x,k[0]]
F[51,x] = F[14,x]*F[22,x]
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_{14}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{51}\! \left(x \right)
F_{4}\! \left(x \right) = F_{14}\! \left(x \right) F_{5}\! \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_{48}\! \left(x , y\right)+F_{49}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{37}\! \left(x , y\right)+F_{39}\! \left(x , y\right)+F_{42}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{10}\! \left(x , y\right) = -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{20}\! \left(x , y\right)+F_{29}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{15}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x , y\right) = -\frac{-y F_{16}\! \left(x , y\right)+F_{16}\! \left(x , 1\right)}{-1+y}
F_{16}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{16}\! \left(x , y\right)^{2} F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = y x
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{15}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x , 1\right)
F_{23}\! \left(x , y\right) = -\frac{-y F_{24}\! \left(x , y\right)+F_{24}\! \left(x , 1\right)}{-1+y}
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)+F_{28}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{28}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{6}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{19}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{35}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{35}\! \left(x \right) = F_{24}\! \left(x , 1\right)
F_{36}\! \left(x , y\right) = -\frac{-y F_{15}\! \left(x , y\right)+F_{15}\! \left(x , 1\right)}{-1+y}
F_{37}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{39}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = -\frac{-y F_{41}\! \left(x , y\right)+F_{41}\! \left(x , 1\right)}{-1+y}
F_{41}\! \left(x , y\right) = -\frac{-y F_{26}\! \left(x , y\right)+F_{26}\! \left(x , 1\right)}{-1+y}
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{42}\! \left(x , y\right)+F_{43}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{45}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = -\frac{-y F_{47}\! \left(x , y\right)+F_{47}\! \left(x , 1\right)}{-1+y}
F_{47}\! \left(x , y\right) = -\frac{-y F_{24}\! \left(x , y\right)+F_{24}\! \left(x , 1\right)}{-1+y}
F_{48}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{19}\! \left(x , y\right) F_{6}\! \left(x , y\right)
F_{51}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \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_14(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_51(x))
Eq(F_4(x), F_14(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_48(x, k_0) + F_49(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_14(x)*F_8(x, k_0))
Eq(F_8(x, k_0), F_1(x) + F_37(x, k_0) + F_39(x, k_0) + F_42(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_14(x))
Eq(F_10(x, k_0), (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_11(x, k_0), F_1(x) + F_12(x, k_0) + F_20(x, k_0) + F_29(x, k_0) + F_33(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x)*F_15(x, k_0)*F_5(x))
Eq(F_14(x), x)
Eq(F_15(x, k_0), (k_0*F_16(x, k_0) - F_16(x, 1))/(k_0 - 1))
Eq(F_16(x, k_0), F_1(x) + F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_16(x, k_0)**2*F_19(x, k_0))
Eq(F_19(x, k_0), k_0*x)
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_14(x)*F_15(x, k_0)*F_22(x))
Eq(F_22(x), F_23(x, 1))
Eq(F_23(x, k_0), (-k_0*F_24(x, k_0) + F_24(x, 1))/(1 - k_0))
Eq(F_24(x, k_0), F_1(x) + F_25(x, k_0) + F_31(x, k_0))
Eq(F_25(x, k_0), F_14(x)*F_26(x, k_0))
Eq(F_26(x, k_0), F_1(x) + F_27(x, k_0) + F_28(x, k_0) + F_29(x, k_0))
Eq(F_27(x, k_0), F_11(x, k_0)*F_14(x))
Eq(F_28(x, k_0), F_14(x)*F_8(x, k_0))
Eq(F_24(x, k_0), F_1(x) + F_29(x, k_0) + F_30(x, k_0))
Eq(F_30(x, k_0), F_14(x)*F_6(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_16(x, k_0)*F_19(x, k_0)*F_24(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_14(x)*F_35(x)*F_36(x, k_0))
Eq(F_35(x), F_24(x, 1))
Eq(F_36(x, k_0), (k_0*F_15(x, k_0) - F_15(x, 1))/(k_0 - 1))
Eq(F_37(x, k_0), F_14(x)*F_38(x, k_0))
Eq(F_38(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_39(x, k_0), F_14(x)*F_40(x, k_0))
Eq(F_40(x, k_0), (k_0*F_41(x, k_0) - F_41(x, 1))/(k_0 - 1))
Eq(F_41(x, k_0), (k_0*F_26(x, k_0) - F_26(x, 1))/(k_0 - 1))
Eq(F_6(x, k_0), F_1(x) + F_42(x, k_0) + F_43(x, k_0) + F_45(x, k_0))
Eq(F_43(x, k_0), F_14(x)*F_44(x, k_0))
Eq(F_44(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_45(x, k_0), F_14(x)*F_46(x, k_0))
Eq(F_46(x, k_0), (k_0*F_47(x, k_0) - F_47(x, 1))/(k_0 - 1))
Eq(F_47(x, k_0), (k_0*F_24(x, k_0) - F_24(x, 1))/(k_0 - 1))
Eq(F_48(x, k_0), F_11(x, k_0)*F_14(x))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_16(x, k_0)*F_19(x, k_0)*F_6(x, k_0))
Eq(F_51(x), F_14(x)*F_22(x))
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:
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