01324_01342_03124_03142_03214_30124_30142_30214_32014
Counting sequence:
1, 1, 2, 6, 24, 111, 546, 2764, 14248, 74531, 394938, 2116832, 11460212, 62586953, 344405986, 1907837118, 10630460276, 59540994862, 335036426764, 1893107096784, 10737184873164, 61106414366449, 348845593306946, 1997171117676286, 11463898688788644, 65962273243149451, 380387542470337322, 2198133654101614664, 12726710138215416972, 73816923453653629463, 428866857792685087282, 2495569437303392629932, 14543052685821465964968, 84867636449674706015466, 495900359737751368490132, 2901219852831088001410796, 16993056156507590841298080, 99641453080208205122554114, 584872887590204540035948972, 3436472396888110786346189024, 20210307299820407731664320592, 118965751161041078821406592679, 700876733119675999660671705978, 4132519744134274773250773222196, 24385177882228604833715322806116, 143999093662034605630245019690271, 850947038413152425795663100641746, 5032006871441626797669135096088644, 29775812934407446467254850545326808, 176302415652004693239092690265451866, 1044514180338619574021487812591106708, 6191868103832204993832952730801728656, 36725756458227891205037914972924928652, 217947783112594442106824728073915938521, 1294071487234198640538785843206074400274, 7687411044248403046022022116581752814926, 45688858363795843373476248420329373711396, 271669962431922245679664265095782271634949, 1616096053346729560505154589553119485532998, 9617903427107455371257504923162468811237616, 57263137366650366106429046713860656325049188, 341071508415827600517503221742769774887236041, 2032290081126136372031154631451729527595293602, 12114083069386502806098732458981275090350935502, 72236198503758043921275759222253067156212097364, 430897355724418947872262921173528879951188228602, 2571240685799679495857554160961312422251749649204, 15348189150635102072996818610203176676338907203068, 91645851410221010644983807668983318719619107654256, 547401099022931515633648972666600900471421447857206, 3270632977682127532397641051611789351309523665711956, 19547333266728122787802633303058490947459909444176856, 116860894298542063391152313568820672991766603690483984, 698833063485064183650907764220192732409452852900510498, 4180198843577671707673203818929912320273807634497533276, 25011315393569469988279814897989934905912117220532592848, 149688757018678650822381046259734859168959988093380002936, 896090697034378803473418154534275768057318215078724118062, 5365646827642060194501679278302532245143830130195113842796, 32136370399470310712918701430631031213549884146504261226844, 192518996486078998620600996876920092675376845580500224193576, 1153585722204723771406862018595777774231321277149199007507876, 6913902622423466798447392414913371275698542538895769955912424, 41446839587013420743687000540501506289434784761252323064867988, 248514716700080998494867634797813843800174544288100659365380276, 1490401118721711743053940251604101758831071626906136596429613253, 8940102461325937120390967353343376493413358987098013464373691442, 53637444445873124618668697822779802855624706862289836067645182122, 321868118615184230362953033075788044422041655164107486237467644588, 1931836031317670476673382529179777347146880184447725833109309004041, 11596933219059945931283014680235164472812821961082260702132711978078, 69629757277310541830780169937322532806546614250962053057952960530736, 418141941134541543348789459374581487719165639695758185246024550132452, 2511470344871777274132869813326233110577822739494005598843470964636529, 15087116809460925825062957383252426099126552684988503651008624221840994, 90647697599162912655413743943570607443941041134907739143356008952253654, 544726030288765868876491575168104758110052748726851578212587565286321924, 3273925951537918505103829005927375180029654779481030725317230223347888306, 19680110768230662438708285393020868391863257019366655947956234237175496004, 118318544861759227938138090017700029330825962676459052050069510110099443164, 711448339691116106672699576097049409511095122368952440182031938629767519024
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24189/
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[7,x]
F[3,x] = F[4,x,1]
F[4,x,k[0]] = F[1,x]+F[5,x,k[0]]+F[8,x,k[0]]
F[5,x,k[0]] = F[6,x,k[0]]*F[7,x]
F[6,x,k[0]] = 1/(-1+k[0])*(F[4,x,k[0]]*k[0]-F[4,x,1])
F[7,x] = x
F[8,x,k[0]] = F[26,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,1,k[0]]
F[10,x,k[0],k[1]] = F[11,x,k[0]*k[1],k[1]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[15,x,k[0],k[1]]+F[35,x,k[0],k[1]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[7,x]
F[13,x,k[0],k[1]] = 1/(-1+k[0])*(F[14,x,k[0],k[1]]*k[0]-F[14,x,1,k[1]])
F[14,x,k[0],k[1]] = F[1,x]+F[15,x,k[0],k[1]]+F[35,x,k[0],k[1]]+F[5,x,k[0]]
F[15,x,k[0],k[1]] = F[16,x,k[0],k[1]]*F[26,x,k[0]]
F[16,x,k[0],k[1]] = F[1,x]+F[17,x,k[0]]+F[19,x,k[0]]+F[21,x,k[0],k[1]]+F[33,x,k[0],k[1]]
F[17,x,k[0]] = F[18,x,1,k[0]]
F[18,x,k[0],k[1]] = F[12,x,k[0]*k[1],k[1]]
F[19,x,k[0]] = F[20,x,1,k[0]]
F[20,x,k[0],k[1]] = F[15,x,k[0]*k[1],k[1]]
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[23,x,k[0]]*F[26,x,k[0]]*F[27,x,k[0],k[1]]*F[4,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]]*F[26,x,k[0]]
F[26,x,k[0]] = k[0]*x
F[27,x,k[0],k[1]] = (F[28,x,k[0]]*k[0]-F[28,x,k[1]]*k[1])/(-k[1]+k[0])
F[28,x,k[0]] = F[1,x]+F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[26,x,k[0]]*F[31,x,k[0]]
F[31,x,k[0]] = F[28,x,k[0]]+F[32,x,k[0]]
F[32,x,k[0]] = F[29,x,k[0]]
F[33,x,k[0],k[1]] = F[34,x,k[0],k[1]]
F[34,x,k[0],k[1]] = F[23,x,k[0]]*F[23,x,k[1]]*F[26,x,k[1]]*F[28,x,k[1]]*F[4,x,k[0]]
F[35,x,k[0],k[1]] = F[36,x,k[0],k[1]]
F[36,x,k[0],k[1]] = F[23,x,k[1]]*F[26,x,k[1]]*F[28,x,k[1]]*F[4,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_{7}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{5}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{5}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{6}\! \left(x , y\right) = \frac{y F_{4}\! \left(x , y\right)-F_{4}\! \left(x , 1\right)}{-1+y}
F_{7}\! \left(x \right) = x
F_{8}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , 1, y\right)
F_{10}\! \left(x , y , z\right) = F_{11}\! \left(x , y z , z\right)
F_{11}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{15}\! \left(x , y , z\right)+F_{35}\! \left(x , y , z\right)
F_{12}\! \left(x , y , z\right) = F_{13}\! \left(x , y , z\right) F_{7}\! \left(x \right)
F_{13}\! \left(x , y , z\right) = \frac{y F_{14}\! \left(x , y , z\right)-F_{14}\! \left(x , 1, z\right)}{-1+y}
F_{14}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y , z\right)+F_{35}\! \left(x , y , z\right)+F_{5}\! \left(x , y\right)
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , y , z\right) F_{26}\! \left(x , y\right)
F_{16}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)+F_{19}\! \left(x , y\right)+F_{21}\! \left(x , y , z\right)+F_{33}\! \left(x , y , z\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , 1, y\right)
F_{18}\! \left(x , y , z\right) = F_{12}\! \left(x , y z , z\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , 1, y\right)
F_{20}\! \left(x , y , z\right) = F_{15}\! \left(x , y z , z\right)
F_{21}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = F_{23}\! \left(x , y\right) F_{26}\! \left(x , y\right) F_{27}\! \left(x , y , z\right) F_{4}\! \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) F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = y x
F_{27}\! \left(x , y , z\right) = \frac{y F_{28}\! \left(x , y\right)-z F_{28}\! \left(x , z\right)}{-z +y}
F_{28}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{33}\! \left(x , y , z\right) = F_{34}\! \left(x , y , z\right)
F_{34}\! \left(x , y , z\right) = F_{23}\! \left(x , y\right) F_{23}\! \left(x , z\right) F_{26}\! \left(x , z\right) F_{28}\! \left(x , z\right) F_{4}\! \left(x , y\right)
F_{35}\! \left(x , y , z\right) = F_{36}\! \left(x , y , z\right)
F_{36}\! \left(x , y , z\right) = F_{23}\! \left(x , z\right) F_{26}\! \left(x , z\right) F_{28}\! \left(x , z\right) F_{4}\! \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_7(x))
Eq(F_3(x), F_4(x, 1))
Eq(F_4(x, k_0), F_1(x) + F_5(x, k_0) + F_8(x, k_0))
Eq(F_5(x, k_0), F_6(x, k_0)*F_7(x))
Eq(F_6(x, k_0), (k_0*F_4(x, k_0) - F_4(x, 1))/(k_0 - 1))
Eq(F_7(x), x)
Eq(F_8(x, k_0), F_26(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, 1, k_0))
Eq(F_10(x, k_0, k_1), F_11(x, k_0*k_1, k_1))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_15(x, k_0, k_1) + F_35(x, k_0, k_1))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_7(x))
Eq(F_13(x, k_0, k_1), (k_0*F_14(x, k_0, k_1) - F_14(x, 1, k_1))/(k_0 - 1))
Eq(F_14(x, k_0, k_1), F_1(x) + F_15(x, k_0, k_1) + F_35(x, k_0, k_1) + F_5(x, k_0))
Eq(F_15(x, k_0, k_1), F_16(x, k_0, k_1)*F_26(x, k_0))
Eq(F_16(x, k_0, k_1), F_1(x) + F_17(x, k_0) + F_19(x, k_0) + F_21(x, k_0, k_1) + F_33(x, k_0, k_1))
Eq(F_17(x, k_0), F_18(x, 1, k_0))
Eq(F_18(x, k_0, k_1), F_12(x, k_0*k_1, k_1))
Eq(F_19(x, k_0), F_20(x, 1, k_0))
Eq(F_20(x, k_0, k_1), F_15(x, k_0*k_1, 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_23(x, k_0)*F_26(x, k_0)*F_27(x, k_0, k_1)*F_4(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)*F_26(x, k_0))
Eq(F_26(x, k_0), k_0*x)
Eq(F_27(x, k_0, k_1), (-k_0*F_28(x, k_0) + k_1*F_28(x, k_1))/(-k_0 + k_1))
Eq(F_28(x, k_0), F_1(x) + F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_26(x, k_0)*F_31(x, k_0))
Eq(F_31(x, k_0), F_28(x, k_0) + F_32(x, k_0))
Eq(F_32(x, k_0), F_29(x, k_0))
Eq(F_33(x, k_0, k_1), F_34(x, k_0, k_1))
Eq(F_34(x, k_0, k_1), F_23(x, k_0)*F_23(x, k_1)*F_26(x, k_1)*F_28(x, k_1)*F_4(x, k_0))
Eq(F_35(x, k_0, k_1), F_36(x, k_0, k_1))
Eq(F_36(x, k_0, k_1), F_23(x, k_1)*F_26(x, k_1)*F_28(x, k_1)*F_4(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": 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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