01234_01342_02341_12340
Counting sequence:
1, 1, 2, 6, 24, 116, 633, 3747, 23502, 153928, 1042595, 7253909, 51590639, 373708913, 2749481916, 20501067566, 154651658986, 1178614586112, 9064065693291, 70272758739185, 548792770570731, 4314043621954301, 34115785657947632, 271266177780329272, 2167748203847482685, 17402931468849157953, 140308510263422695458, 1135686280241629215778, 9226241751195777972548, 75209936357072503068832, 615052571353995124968713, 5044846760668934888010635, 41495667845725896493974018, 342218991195329385339861536, 2829345013936805098891659995, 23447021294900187972260584457, 194739442918119911788276879403, 1620815615496624625540832401565, 13516980836644888407368875875776, 112940241665638401007486520533232, 945366935185790603221349008050989, 7926791691829562622638982749930753, 66574071079853899840171985821829666, 560003959499779406909717555220638594, 4717644858032116038284462649784100652, 39799662323129736984289604058479650376, 336222806031793518664995599286421872221, 2844093602223881061635095322455543960157, 24088311371561871347376903003134369541785, 204264453199041893937286591183734374345369, 1734134204594542425369325738732658763527882, 14738618222080246414585460981641447641364574, 125399779653597552494964291940612471830015400, 1068035070282375384471965828178216216079185372, 9105561389606078831051623116661752671117968257, 77704294567104555590712270938820821532765524267, 663721398267912353386109023411341775339845974766, 5674339195920341814039373861973154517633470117920, 48553475274624300992366107286083329843626769858107, 415803781820007266385914215231321973094362867762245, 3563754533767003195286306469831371642549989075845143, 30568004126926162227169155733591127958174639762222641, 262395022530377454451460075018076611337229475705837508, 2254047528934827979735344499810915628874960598887795518, 19376696858141639692434036080064886737095322567870386738, 166684913311935883759580023984817268228286842202559605088, 1434841093500199723474465503744493554142917128908455459323, 12359296940441566183480090230365363089706783503052905816313, 106526590540704091359510054738839705757881293094969238809003, 918731886658660025049881285084465079543292737547106818790909, 7928272778062279809581281159194056108321396754123645432695360, 68457376283707476938256253062686836767768099045086524316404528, 591434864956635149848202470770534250831924695677585188309019669, 5112484593350248201988786983306558679015722480960525469991366713, 44216991868973341704695545400955057839919268631415502305228755690, 382624160799989216108179487420172546097605737283727371703319854874, 3312651585980689821784848960652145688020945027368032198829923792596, 28694171416327671976961698979776024780296354297494671104954034247936, 248668496956665424761148955919376315316218656552377048507986232854469, 2156015114539009005902894512738942622241338067120437289865735991968413, 18701729604480949569726314230795464212619572710730756441360054359064529, 162295268633815979157914273517336509506294360746815560900547870780855737, 1409027288507233365111142487945224236676678329637620148368740834623727546, 12238210548553095934529095870525534529869770727171333810158046838142716422, 106340103416238437675946824476967101245121499452849815872781246609160362896, 924384591407618906758771861590093582634825115907875681643058276912558901468, 8038605989288294973785086515841821254463218642253404228238285704508420969345, 69932219733658178640676931133467168517704956944550643194841160148242983165363, 608609382153252816475858754950682466332946423750882057406594837223825505515342, 5298599424891291379234528317961755624638213492622993903958487270705981970055432, 46146750525895623042364715842342030286857808103502540838186698830722796737875523, 402045629583451805850223656481861751341644970220633736946486774079345993544877925, 3503970570057967835331198261443677512649966623313153915549488755448737314746797303, 30548735888353600635499624952134356436160404632587360695611120443682208372993970153, 266422336871079863431685340585533941988675690094943963950237616752885226912313709584, 2324286291873790726301833160496274983603293137879762816186917153829734380811700667696, 20283705720510251112938602350874272221308219930196756649871614790922208223696032832049, 177068316172962501972941696040668469266329880546953007156730622778055322084400211703577, 1546206725753775986889326104666037414192101011685480427677505279099645688959918159785434, 13505938040485743767743091599442027591394679742534087093754051790154220926629051020012566, 118007570865421527419484964058919237345383192419617396825567238916210287581757482170820008
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/24060/
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[9,x]
F[3,x] = F[1,x]+F[4,x]+F[43,x]
F[4,x] = F[5,x]*F[9,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[37,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,k[0]]*F[9,x]
F[8,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[9,x] = x
F[10,x,k[0]] = F[11,x,k[0]]*F[18,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0],1]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[0]*k[1]]
F[13,x,k[0],k[1]] = F[1,x]+F[14,x,k[0],k[1]]+F[16,x,k[0],k[1]]+F[19,x,k[0],k[1]]+F[35,x,k[0],k[1]]
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[9,x]
F[15,x,k[0],k[1]] = 1/(-1+k[0])*(F[13,x,k[0],k[1]]*k[0]-F[13,x,1,k[1]])
F[16,x,k[0],k[1]] = F[17,x,k[0],k[1]]*F[18,x,k[0]]
F[17,x,k[0],k[1]] = (F[12,x,k[0],1]*k[0]-F[12,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[18,x,k[0]] = k[0]*x
F[19,x,k[0],k[1]] = F[18,x,k[1]]*F[20,x,k[0],k[1]]
F[20,x,k[0],k[1]] = F[1,x]+F[19,x,k[0],k[1]]+F[21,x,k[0],k[1]]+F[23,x,k[0],k[1]]+F[26,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[9,x]
F[22,x,k[0],k[1]] = 1/(-1+k[0])*(F[20,x,k[0],k[1]]*k[0]-F[20,x,1,k[1]])
F[23,x,k[0],k[1]] = F[18,x,k[0]]*F[24,x,k[0],k[1]]
F[24,x,k[0],k[1]] = (F[25,x,k[0],1]*k[0]-F[25,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[25,x,k[0],k[1]] = F[20,x,k[0],k[0]*k[1]]
F[26,x,k[0],k[1]] = F[27,x,k[0],k[1]]*F[9,x]
F[27,x,k[0],k[1]] = (F[28,x,k[0],k[1]]*k[1]-F[28,x,k[0],1])/(-1+k[1])
F[28,x,k[0],k[1]] = F[1,x]+F[29,x,k[0],k[1]]+F[31,x,k[0],k[1]]+F[34,x,k[0],k[1]]
F[29,x,k[0],k[1]] = F[30,x,k[0],k[1]]*F[9,x]
F[30,x,k[0],k[1]] = 1/(-1+k[0])*(F[28,x,k[0],k[1]]*k[0]-F[28,x,1,k[1]])
F[31,x,k[0],k[1]] = F[18,x,k[0]]*F[32,x,k[0],k[1]]
F[32,x,k[0],k[1]] = (F[33,x,k[0],1]*k[0]-F[33,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[33,x,k[0],k[1]] = F[28,x,k[0],k[0]*k[1]]
F[34,x,k[0],k[1]] = F[18,x,k[1]]*F[28,x,k[0],k[1]]
F[35,x,k[0],k[1]] = F[36,x,k[0],k[1]]*F[9,x]
F[36,x,k[0],k[1]] = (F[20,x,k[0],k[1]]*k[1]-F[20,x,k[0],1])/(-1+k[1])
F[37,x,k[0]] = F[38,x,k[0]]*F[9,x]
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[10,x,k[0]]+F[40,x,k[0]]+F[42,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]*F[9,x]
F[41,x,k[0]] = 1/(-1+k[0])*(F[39,x,k[0]]*k[0]-F[39,x,1])
F[42,x,k[0]] = F[19,x,k[0],1]
F[43,x] = F[44,x]*F[9,x]
F[44,x] = F[39,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_{9}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{43}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{9}\! \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_{10}\! \left(x , y\right)+F_{37}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{8}\! \left(x , y\right) = \frac{F_{6}\! \left(x , y\right) y -F_{6}\! \left(x , 1\right)}{-1+y}
F_{9}\! \left(x \right) = x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y , 1\right)
F_{12}\! \left(x , y , z\right) = F_{13}\! \left(x , y , y z \right)
F_{13}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y , z\right)+F_{16}\! \left(x , y , z\right)+F_{19}\! \left(x , y , z\right)+F_{35}\! \left(x , y , z\right)
F_{14}\! \left(x , y , z\right) = F_{15}\! \left(x , y , z\right) F_{9}\! \left(x \right)
F_{15}\! \left(x , y , z\right) = \frac{F_{13}\! \left(x , y , z\right) y -F_{13}\! \left(x , 1, z\right)}{-1+y}
F_{16}\! \left(x , y , z\right) = F_{17}\! \left(x , y , z\right) F_{18}\! \left(x , y\right)
F_{17}\! \left(x , y , z\right) = \frac{F_{12}\! \left(x , y , 1\right) y -F_{12}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y , z\right) = F_{18}\! \left(x , z\right) F_{20}\! \left(x , y , z\right)
F_{20}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y , z\right)+F_{21}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)+F_{26}\! \left(x , y , z\right)
F_{21}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right) F_{9}\! \left(x \right)
F_{22}\! \left(x , y , z\right) = \frac{F_{20}\! \left(x , y , z\right) y -F_{20}\! \left(x , 1, z\right)}{-1+y}
F_{23}\! \left(x , y , z\right) = F_{18}\! \left(x , y\right) F_{24}\! \left(x , y , z\right)
F_{24}\! \left(x , y , z\right) = \frac{F_{25}\! \left(x , y , 1\right) y -F_{25}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}
F_{25}\! \left(x , y , z\right) = F_{20}\! \left(x , y , y z \right)
F_{26}\! \left(x , y , z\right) = F_{27}\! \left(x , y , z\right) F_{9}\! \left(x \right)
F_{27}\! \left(x , y , z\right) = \frac{F_{28}\! \left(x , y , z\right) z -F_{28}\! \left(x , y , 1\right)}{-1+z}
F_{28}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y , z\right)+F_{31}\! \left(x , y , z\right)+F_{34}\! \left(x , y , z\right)
F_{29}\! \left(x , y , z\right) = F_{30}\! \left(x , y , z\right) F_{9}\! \left(x \right)
F_{30}\! \left(x , y , z\right) = \frac{F_{28}\! \left(x , y , z\right) y -F_{28}\! \left(x , 1, z\right)}{-1+y}
F_{31}\! \left(x , y , z\right) = F_{18}\! \left(x , y\right) F_{32}\! \left(x , y , z\right)
F_{32}\! \left(x , y , z\right) = \frac{F_{33}\! \left(x , y , 1\right) y -F_{33}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}
F_{33}\! \left(x , y , z\right) = F_{28}\! \left(x , y , y z \right)
F_{34}\! \left(x , y , z\right) = F_{18}\! \left(x , z\right) F_{28}\! \left(x , y , z\right)
F_{35}\! \left(x , y , z\right) = F_{36}\! \left(x , y , z\right) F_{9}\! \left(x \right)
F_{36}\! \left(x , y , z\right) = \frac{F_{20}\! \left(x , y , z\right) z -F_{20}\! \left(x , y , 1\right)}{-1+z}
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{38}\! \left(x , y\right) = \frac{F_{39}\! \left(x , y\right) y -F_{39}\! \left(x , 1\right)}{-1+y}
F_{39}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{40}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{41}\! \left(x , y\right) = \frac{F_{39}\! \left(x , y\right) y -F_{39}\! \left(x , 1\right)}{-1+y}
F_{42}\! \left(x , y\right) = F_{19}\! \left(x , y , 1\right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right) F_{9}\! \left(x \right)
F_{44}\! \left(x \right) = F_{39}\! \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_9(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_43(x))
Eq(F_4(x), F_5(x)*F_9(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_10(x, k_0) + F_37(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, k_0)*F_9(x))
Eq(F_8(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_9(x), x)
Eq(F_10(x, k_0), F_11(x, k_0)*F_18(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0, 1))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_0*k_1))
Eq(F_13(x, k_0, k_1), F_1(x) + F_14(x, k_0, k_1) + F_16(x, k_0, k_1) + F_19(x, k_0, k_1) + F_35(x, k_0, k_1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1)*F_9(x))
Eq(F_15(x, k_0, k_1), (k_0*F_13(x, k_0, k_1) - F_13(x, 1, k_1))/(k_0 - 1))
Eq(F_16(x, k_0, k_1), F_17(x, k_0, k_1)*F_18(x, k_0))
Eq(F_17(x, k_0, k_1), (-k_0*F_12(x, k_0, 1) + k_1*F_12(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0, k_1), F_18(x, k_1)*F_20(x, k_0, k_1))
Eq(F_20(x, k_0, k_1), F_1(x) + F_19(x, k_0, k_1) + F_21(x, k_0, k_1) + F_23(x, k_0, k_1) + F_26(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1)*F_9(x))
Eq(F_22(x, k_0, k_1), (k_0*F_20(x, k_0, k_1) - F_20(x, 1, k_1))/(k_0 - 1))
Eq(F_23(x, k_0, k_1), F_18(x, k_0)*F_24(x, k_0, k_1))
Eq(F_24(x, k_0, k_1), (-k_0*F_25(x, k_0, 1) + k_1*F_25(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_25(x, k_0, k_1), F_20(x, k_0, k_0*k_1))
Eq(F_26(x, k_0, k_1), F_27(x, k_0, k_1)*F_9(x))
Eq(F_27(x, k_0, k_1), (-k_1*F_28(x, k_0, k_1) + F_28(x, k_0, 1))/(1 - k_1))
Eq(F_28(x, k_0, k_1), F_1(x) + F_29(x, k_0, k_1) + F_31(x, k_0, k_1) + F_34(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), F_30(x, k_0, k_1)*F_9(x))
Eq(F_30(x, k_0, k_1), (k_0*F_28(x, k_0, k_1) - F_28(x, 1, k_1))/(k_0 - 1))
Eq(F_31(x, k_0, k_1), F_18(x, k_0)*F_32(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), (-k_0*F_33(x, k_0, 1) + k_1*F_33(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_33(x, k_0, k_1), F_28(x, k_0, k_0*k_1))
Eq(F_34(x, k_0, k_1), F_18(x, k_1)*F_28(x, k_0, k_1))
Eq(F_35(x, k_0, k_1), F_36(x, k_0, k_1)*F_9(x))
Eq(F_36(x, k_0, k_1), (-k_1*F_20(x, k_0, k_1) + F_20(x, k_0, 1))/(1 - k_1))
Eq(F_37(x, k_0), F_38(x, k_0)*F_9(x))
Eq(F_38(x, k_0), (-k_0*F_39(x, k_0) + F_39(x, 1))/(1 - k_0))
Eq(F_39(x, k_0), F_1(x) + F_10(x, k_0) + F_40(x, k_0) + F_42(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0)*F_9(x))
Eq(F_41(x, k_0), (k_0*F_39(x, k_0) - F_39(x, 1))/(k_0 - 1))
Eq(F_42(x, k_0), F_19(x, k_0, 1))
Eq(F_43(x), F_44(x)*F_9(x))
Eq(F_44(x), F_39(x, 1))
Pack JSON:
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Specification JSON:
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