01234_01324_01342_02134_02314_03124_03142_03214_30124_30142_30214
Counting sequence:
1, 1, 2, 6, 24, 109, 522, 2579, 13054, 67399, 353618, 1879532, 10097186, 54733019, 298974586, 1644021492, 9092937786, 50550286238, 282303196066, 1582965381032, 8908681086244, 50302611736159, 284886896690220, 1617879300592708, 9211124019110402, 52563603048743364, 300598506175506372, 1722461336963585467, 9888085878177505420, 56861783479305206791, 327510404534828743426, 1889216486994654785947, 10913150133766745816936, 63123886712494593687135, 365577255965653152828616, 2119707434923565472209378, 12304274364273937557530280, 71497965858175843447945973, 415877329691897970655379082, 2421301016505224547240834455, 14109902898545588210907012274, 82294756812747877579825207949, 480369844770787371835790163376, 2806199051942367370079263862831, 16405339115523735548863773375900, 95975810678651359195577022509680, 561868850565671899769489423683042, 3291488187212506855066556076208691, 19293995808751931116758324936647720, 113165397822389645581006962998259145, 664135102693800979634563455670434596, 3899786502331209679218156016775650864, 22911720669853968889231145240267705562, 134678549804089639160259872603100320614, 792054116410756421864888109986620503796, 4660357843430835882370938940813799528539, 27433698142632034054427811251438719688322, 161563481321228799070370916270929373056163, 951895415393216577460949918228693834079252, 5610689208509745061237944050658427486755341, 33084014521874623796825615099003948155817098, 195159439279659858707147282127885240554960501, 1151661676039391288450166246013947876804559524, 6798594545485846065871225464165230385660348077, 40148318138325109406530276218337068315052906270, 237172810286626309043938770346620151394523667585, 1401545874935554815241371688988107855451134243808, 8284958841661125523393797274616562634051900823525, 48990282409180778227050448924333628536483901264604, 289775848162230899953272928046668023203014100169082, 1714523148530537747219820977285411949556389759022454, 10147285292006259964009684205603941738807612637955065, 60072860368173336774091006363572497613431126957502850, 355734008882759754217187252387015534949673681043808801, 2107113550070601700779555908216005044977818044732395454, 12484263870272686843580533998894489053670630459063681368, 73985646240951179097935294660822321131429992764598299846, 438569812184799963861326516017930781366817687495064155905, 2600363336593687119520777498608425857063938183525441228654, 15421647625284973818045622365153521822108300754456523523496, 91480064300771769397864602695865681068061314770740072104798, 542773560988739583287849847537049941153717989751684860879572, 3221106812151480007171272919732882754164111716780559099799284, 19119809003403797304446915871095976305544838158824222615619697, 113514619243448717902411648751586502074506359307809880521267638, 674074324652664490270512986940445119519030146287175698115046920, 4003589157394297227174095962150503059428760042874343334238865910, 23783458699227743744688598779083067374075030625696983617470319814, 141313102426701887711183882627447756118001708165679276908381408984, 839788547266748575531885627329089995148825989718832058793524531788, 4991554379988097600599150957592971112560112446950818815783779154266, 29674151630236168196382986903137894877396878383542989783369447237815, 176439500231320826500069432551267243899312900584901709806199439027974, 1049268750507236544027609622787790901975962414315742799747971281068677, 6240933154939818308154105155089299870256260538708801492746803142318708, 37126388366492186442977594890359046716029141912233319241559756964860499, 220894452880761911884601987592975212132851782848918021206193421954008770, 1314481411569372622343055575810739198000728996438509669697459302586390563, 7823304983837319469321874395538139945626946614037331874817888346163754742, 46568358284534187061046081694112066121445685848621278922089810535323742112, 277239539634649913846116854501260744736777981465382635038768859120558387764
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/24236/
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[21,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[34,x,k[0],k[1]]+F[37,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]] = F[14,x,1,k[0],k[1]]
F[14,x,k[0],k[1],k[2]] = F[1,x]+F[15,x,k[0],k[1],k[2]]+F[17,x,k[0],k[1],k[2]]+F[22,x,k[0],k[1],k[2]]+F[31,x,k[0],k[1],k[2]]
F[15,x,k[0],k[1],k[2]] = F[16,x,k[0],k[1],k[2]]*F[7,x]
F[16,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[14,x,k[0],k[1],k[2]]*k[0]-F[14,x,1,k[1],k[2]])
F[17,x,k[0],k[1],k[2]] = F[18,x,k[0],k[1],k[2]]*F[21,x,k[0]]
F[18,x,k[0],k[1],k[2]] = (F[19,x,k[0],k[1]]*k[1]-F[19,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[19,x,k[0],k[1]] = (F[20,x,k[0],1]*k[0]-F[20,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[20,x,k[0],k[1]] = F[11,x,k[0],k[0]*k[1]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0],k[1],k[2]] = F[23,x,k[0],k[1],k[2]]
F[23,x,k[0],k[1],k[2]] = F[21,x,k[1]]*F[24,x,k[0],k[1],k[2]]
F[24,x,k[0],k[1],k[2]] = (-F[25,x,1,k[1],k[2]]*k[1]+F[25,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[25,x,k[0],k[1],k[2]] = F[10,x,k[0],k[1]]+F[26,x,k[0],k[1],k[2]]
F[26,x,k[0],k[1],k[2]] = F[27,x,k[0],k[1],k[2]]
F[27,x,k[0],k[1],k[2]] = F[21,x,k[2]]*F[28,x,k[1]]*F[28,x,k[2]]*F[4,x,k[1]]
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[21,x,k[0]]*F[28,x,k[0]]
F[31,x,k[0],k[1],k[2]] = F[32,x,k[0],k[1],k[2]]
F[32,x,k[0],k[1],k[2]] = F[28,x,k[2]]^2*F[21,x,k[2]]*F[33,x,k[0],k[1]]
F[33,x,k[0],k[1]] = (F[4,x,k[0]]*k[0]-F[4,x,k[1]]*k[1])/(-k[1]+k[0])
F[34,x,k[0],k[1]] = F[35,x,k[0],k[1]]
F[35,x,k[0],k[1]] = F[21,x,k[0]]*F[36,x,k[0],k[1]]
F[36,x,k[0],k[1]] = F[25,x,1,k[0],k[1]]
F[37,x,k[0],k[1]] = F[38,x,k[0],k[1]]
F[38,x,k[0],k[1]] = F[28,x,k[1]]^2*F[21,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_{0}\right) = F_{1}\! \left(x \right)+F_{5}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{5}\! \left(x , y_{0}\right) = F_{6}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)
F_{6}\! \left(x , y_{0}\right) = \frac{F_{4}\! \left(x , y_{0}\right) y_{0}-F_{4}\! \left(x , 1\right)}{-1+y_{0}}
F_{7}\! \left(x \right) = x
F_{8}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , 1, y_{0}\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{34}\! \left(x , y_{0}, y_{1}\right)+F_{37}\! \left(x , y_{0}, y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{1}\right) F_{7}\! \left(x \right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , 1, y_{0}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{7}\! \left(x \right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}-F_{14}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{21}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{19}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{19}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{19}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{20}\! \left(x , y_{0}, 1\right) y_{0}-F_{20}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{21}\! \left(x , y_{0}\right) = y_{0} x
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{1}\right) F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{-F_{25}\! \left(x , 1, y_{1}, y_{2}\right) y_{1}+F_{25}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right) y_{0}}{-y_{1}+y_{0}}
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x , y_{0}, y_{1}\right)+F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{2}\right) F_{28}\! \left(x , y_{1}\right) F_{28}\! \left(x , y_{2}\right) F_{4}\! \left(x , y_{1}\right)
F_{28}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}\right)
F_{29}\! \left(x , y_{0}\right) = F_{30}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{28}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{2}\right)^{2} F_{21}\! \left(x , y_{2}\right) F_{33}\! \left(x , y_{0}, y_{1}\right)
F_{33}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{4}\! \left(x , y_{0}\right) y_{0}-F_{4}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{34}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , y_{0}, y_{1}\right)
F_{35}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{0}\right) F_{36}\! \left(x , y_{0}, y_{1}\right)
F_{36}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x , 1, y_{0}, y_{1}\right)
F_{37}\! \left(x , y_{0}, y_{1}\right) = F_{38}\! \left(x , y_{0}, y_{1}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{1}\right)^{2} F_{21}\! \left(x , y_{1}\right) F_{4}\! \left(x , y_{0}\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_21(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_34(x, k_0, k_1) + F_37(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), F_14(x, 1, k_0, k_1))
Eq(F_14(x, k_0, k_1, k_2), F_1(x) + F_15(x, k_0, k_1, k_2) + F_17(x, k_0, k_1, k_2) + F_22(x, k_0, k_1, k_2) + F_31(x, k_0, k_1, k_2))
Eq(F_15(x, k_0, k_1, k_2), F_16(x, k_0, k_1, k_2)*F_7(x))
Eq(F_16(x, k_0, k_1, k_2), (k_0*F_14(x, k_0, k_1, k_2) - F_14(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_17(x, k_0, k_1, k_2), F_18(x, k_0, k_1, k_2)*F_21(x, k_0))
Eq(F_18(x, k_0, k_1, k_2), (-k_1*F_19(x, k_0, k_1) + k_2*F_19(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_19(x, k_0, k_1), (-k_0*F_20(x, k_0, 1) + k_1*F_20(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1), F_11(x, k_0, k_0*k_1))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0, k_1, k_2), F_23(x, k_0, k_1, k_2))
Eq(F_23(x, k_0, k_1, k_2), F_21(x, k_1)*F_24(x, k_0, k_1, k_2))
Eq(F_24(x, k_0, k_1, k_2), (-k_0*F_25(x, k_0/k_1, k_1, k_2) + k_1*F_25(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_25(x, k_0, k_1, k_2), F_10(x, k_0, k_1) + F_26(x, k_0, k_1, k_2))
Eq(F_26(x, k_0, k_1, k_2), F_27(x, k_0, k_1, k_2))
Eq(F_27(x, k_0, k_1, k_2), F_21(x, k_2)*F_28(x, k_1)*F_28(x, k_2)*F_4(x, 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_21(x, k_0)*F_28(x, k_0))
Eq(F_31(x, k_0, k_1, k_2), F_32(x, k_0, k_1, k_2))
Eq(F_32(x, k_0, k_1, k_2), F_21(x, k_2)*F_28(x, k_2)**2*F_33(x, k_0, k_1))
Eq(F_33(x, k_0, k_1), (-k_0*F_4(x, k_0) + k_1*F_4(x, k_1))/(-k_0 + k_1))
Eq(F_34(x, k_0, k_1), F_35(x, k_0, k_1))
Eq(F_35(x, k_0, k_1), F_21(x, k_0)*F_36(x, k_0, k_1))
Eq(F_36(x, k_0, k_1), F_25(x, 1, k_0, k_1))
Eq(F_37(x, k_0, k_1), F_38(x, k_0, k_1))
Eq(F_38(x, k_0, k_1), F_21(x, k_1)*F_28(x, k_1)**2*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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