01234_01243_01324_01342_01423_01432_02134_02143_02341_02431_03142_03241
Counting sequence:
1, 1, 2, 6, 24, 108, 517, 2569, 13066, 67476, 352165, 1852023, 9794687, 52021852, 277211870, 1481027073, 7928884941, 42519390927, 228325916173, 1227476294053, 6605091804738, 35570250964278, 191683344411820, 1033541732553745, 5575480824508506, 30089700757954299, 162446395287966900, 877280196669674278, 4738983342100707554, 25605652355698380110, 138381386742013759738, 747996983982519382595, 4043831180629561043383, 21864981643649756619918, 118239107293906081189692, 639474143702787606283088, 3458830852359801305947435, 18710072557021542256467208, 101217899483102271952041189, 547609843002566049464704333, 2962879873321725254106945030, 16031821759999374164263073009, 86751145911332563137586032369, 469449448095066423799398589264, 2540514699100303699306399970461, 13749030295183014013208526281057, 74411198882486904559588196853954, 402734629076400323267672521009842, 2179780658438328224890899589380816, 11798277381633308713712970250104453, 63860946348036155591114168539838198, 345670320728300905991718673572841084, 1871104209896245288104342808919037947, 10128432236009953935921222795888339216, 54826957277266071951366877602185642633, 296792617125426128707907334211030793648, 1606639705931204553850499091951969333515, 8697407653621608196566527003365060201848, 47083268806015404411880981905674457135197, 254887419703679736604747467578513883136030, 1379859320078929735624248385873975297362541, 7470083817202980754572847841215160239285080, 40440829898785847562859314559054788484383611, 218936545418635249868487013666875566019737734, 1185276849851570420396773046740378664491515359, 6416887529942976981029904139014432358248276823, 34740167114437206438046875692457242203679673379, 188079739722870342970429435210873131771830832025, 1018250344988159547393939564704081094443956430028, 5512763665067963093341933803286940355158015936192, 29846009586935204449814890773260769716750998531062, 161586513940794532110324498853092783114292518878864, 874834185726121993820937335151749990148406392146733, 4736396437189635008803212758630140764264006403720725, 25643180668875801322757162952178710209804808851071043, 138834427593341301608560609116423447494850298005475335, 751664066225078065017707370007656338024451188885422364, 4069599231672978100680163902307237999642860808017889409, 22033355796445143361918580596549134926670241682628576565, 119291836047320534580901872811989532482534847685214113185, 645865065149983384745516116806607286691495154869127174492, 3496824143481080205127741647226251029239805386441745532113, 18932442759639510358532974510448812574954921507575142258720, 102503882681942392303144897377585694233723805353895743048940, 554976671501096085048738137555036584995175886477921417995139, 3004760329846574537471763232476080340570964822201580947825122, 16268428229251778216309795758634816779502522905690416059072686, 88080943980422053043335605882605012662264448569294521597110233, 476890740653528182502489498715061334193533835254624079779930250, 2582000649925881078443005242578331935570911724753953237966745561, 13979585553843136050929449104754600860308568133557955013382881182, 75688989052576651493330771604186818715544625808315137324576110330, 409799610909252599600307291399084687322683926006227116211699208379, 2218762307188949312652192421939443446008546621073646527294121903934, 12012969964429533121412700298963401292984473363361071475096886416172, 65041470682018566285560318018790184219196850042883308215818059634088, 352152390667453871195305079535149018547210770064813582043292693401463, 1906651128909056086135618691468614735381017027397733160730341353941700, 10323147067780539627760300121873915994790112910551694777988707096536191, 55892464724097929632737229633550064528588336119299113355249601709372659, 302617931432691846489824171183579998517757465344778781106942280510038419
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/24251/
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[56,x]
F[4,x] = F[5,x]*F[9,x]
F[5,x] = F[1,x]+F[35,x]+F[54,x]+F[6,x]
F[6,x] = F[7,x]*F[9,x]
F[7,x] = F[1,x]+F[10,x]+F[52,x]+F[6,x]+F[8,x]
F[8,x] = F[7,x]*F[9,x]
F[9,x] = x
F[10,x] = F[11,x]*F[9,x]
F[11,x] = F[12,x,1]
F[12,x,k[0]] = (F[13,x,k[0]]*k[0]-F[13,x,1])/(-1+k[0])
F[13,x,k[0]] = F[1,x]+F[14,x,k[0]]+F[16,x,k[0]]+F[20,x,k[0]]+F[21,x,k[0]]
F[14,x,k[0]] = F[13,x,k[0]]*F[15,x,k[0]]
F[15,x,k[0]] = k[0]*x
F[16,x,k[0]] = F[17,x,k[0]]*F[9,x]
F[17,x,k[0]] = (F[18,x,k[0]]*k[0]-F[18,x,1])/(-1+k[0])
F[18,x,k[0]] = F[1,x]+F[19,x,k[0]]+F[20,x,k[0]]+F[21,x,k[0]]+F[6,x]
F[19,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]
F[20,x,k[0]] = F[12,x,k[0]]*F[9,x]
F[21,x,k[0]] = F[22,x,k[0]]*F[9,x]
F[22,x,k[0]] = (F[23,x,k[0]]*k[0]-F[23,x,1])/(-1+k[0])
F[23,x,k[0]] = F[1,x]+F[24,x,k[0]]+F[25,x,k[0]]+F[50,x,k[0]]+F[51,x,k[0]]
F[24,x,k[0]] = F[15,x,k[0]]*F[23,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]*F[9,x]
F[26,x,k[0]] = (F[27,x,k[0]]*k[0]-F[27,x,1])/(-1+k[0])
F[27,x,k[0]] = F[1,x]+F[28,x,k[0]]+F[29,x]+F[31,x]+F[51,x,k[0]]
F[28,x,k[0]] = F[15,x,k[0]]*F[27,x,k[0]]
F[29,x] = F[30,x]*F[9,x]
F[30,x] = F[27,x,1]
F[31,x] = F[32,x]*F[9,x]
F[32,x] = F[33,x,1]
F[33,x,k[0]] = F[1,x]+F[34,x,k[0]]+F[35,x]+F[37,x,k[0]]+F[6,x]
F[34,x,k[0]] = F[15,x,k[0]]*F[33,x,k[0]]
F[35,x] = F[36,x]*F[9,x]
F[36,x] = F[13,x,1]
F[37,x,k[0]] = F[38,x,k[0]]*F[9,x]
F[38,x,k[0]] = F[1,x]+F[39,x,k[0]]+F[40,x]+F[41,x]+F[42,x,k[0]]+F[45,x,k[0]]
F[39,x,k[0]] = F[15,x,k[0]]*F[38,x,k[0]]
F[40,x] = F[24,x,1]
F[41,x] = F[25,x,1]
F[42,x,k[0]] = F[43,x,k[0]]*F[9,x]
F[43,x,k[0]] = (F[44,x,k[0]]*k[0]-F[44,x,1])/(-1+k[0])
F[44,x,k[0]] = (F[33,x,k[0]]*k[0]-F[33,x,1])/(-1+k[0])
F[45,x,k[0]] = F[46,x,k[0]]*F[9,x]
F[46,x,k[0]] = (F[47,x,k[0]]*k[0]-F[47,x,1])/(-1+k[0])
F[47,x,k[0]] = (F[48,x,k[0]]*k[0]-F[48,x,1])/(-1+k[0])
F[48,x,k[0]] = F[1,x]+F[29,x]+F[49,x,k[0]]+F[50,x,k[0]]+F[51,x,k[0]]
F[49,x,k[0]] = F[15,x,k[0]]*F[48,x,k[0]]
F[50,x,k[0]] = F[44,x,k[0]]*F[9,x]
F[51,x,k[0]] = F[47,x,k[0]]*F[9,x]
F[52,x] = F[53,x]*F[9,x]
F[53,x] = F[22,x,1]
F[54,x] = F[55,x]*F[9,x]
F[55,x] = F[23,x,1]
F[56,x] = F[57,x]*F[9,x]
F[57,x] = F[1,x]+F[29,x]+F[31,x]+F[58,x]
F[58,x] = F[59,x]*F[9,x]
F[59,x] = F[48,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_{56}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{9}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{35}\! \left(x \right)+F_{54}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right) F_{9}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)+F_{52}\! \left(x \right)+F_{6}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{7}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = x
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{9}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{12}\! \left(x , y\right) = -\frac{-y F_{13}\! \left(x , y\right)+F_{13}\! \left(x , 1\right)}{-1+y}
F_{13}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{16}\! \left(x , y\right)+F_{20}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = y x
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{9}\! \left(x \right)
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_{21}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{19}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{22}\! \left(x , y\right) = -\frac{-y F_{23}\! \left(x , y\right)+F_{23}\! \left(x , 1\right)}{-1+y}
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{24}\! \left(x , y\right)+F_{25}\! \left(x , y\right)+F_{50}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{26}\! \left(x , y\right) = -\frac{-y F_{27}\! \left(x , y\right)+F_{27}\! \left(x , 1\right)}{-1+y}
F_{27}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y\right)+F_{29}\! \left(x \right)+F_{31}\! \left(x \right)+F_{51}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{9}\! \left(x \right)
F_{30}\! \left(x \right) = F_{27}\! \left(x , 1\right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{9}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x , 1\right)
F_{33}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{35}\! \left(x \right)+F_{37}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{34}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{9}\! \left(x \right)
F_{36}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{38}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{39}\! \left(x , y\right)+F_{40}\! \left(x \right)+F_{41}\! \left(x \right)+F_{42}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{38}\! \left(x , y\right)
F_{40}\! \left(x \right) = F_{24}\! \left(x , 1\right)
F_{41}\! \left(x \right) = F_{25}\! \left(x , 1\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{43}\! \left(x , y\right) = -\frac{-y F_{44}\! \left(x , y\right)+F_{44}\! \left(x , 1\right)}{-1+y}
F_{44}\! \left(x , y\right) = -\frac{-y F_{33}\! \left(x , y\right)+F_{33}\! \left(x , 1\right)}{-1+y}
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right) F_{9}\! \left(x \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_{48}\! \left(x , y\right)+F_{48}\! \left(x , 1\right)}{-1+y}
F_{48}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x \right)+F_{49}\! \left(x , y\right)+F_{50}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{48}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{44}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{51}\! \left(x , y\right) = F_{47}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right) F_{9}\! \left(x \right)
F_{53}\! \left(x \right) = F_{22}\! \left(x , 1\right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right) F_{9}\! \left(x \right)
F_{55}\! \left(x \right) = F_{23}\! \left(x , 1\right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right) F_{9}\! \left(x \right)
F_{57}\! \left(x \right) = F_{1}\! \left(x \right)+F_{29}\! \left(x \right)+F_{31}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right) F_{9}\! \left(x \right)
F_{59}\! \left(x \right) = F_{48}\! \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_56(x))
Eq(F_4(x), F_5(x)*F_9(x))
Eq(F_5(x), F_1(x) + F_35(x) + F_54(x) + F_6(x))
Eq(F_6(x), F_7(x)*F_9(x))
Eq(F_7(x), F_1(x) + F_10(x) + F_52(x) + F_6(x) + F_8(x))
Eq(F_8(x), F_7(x)*F_9(x))
Eq(F_9(x), x)
Eq(F_10(x), F_11(x)*F_9(x))
Eq(F_11(x), F_12(x, 1))
Eq(F_12(x, k_0), (-k_0*F_13(x, k_0) + F_13(x, 1))/(1 - k_0))
Eq(F_13(x, k_0), F_1(x) + F_14(x, k_0) + F_16(x, k_0) + F_20(x, k_0) + F_21(x, k_0))
Eq(F_14(x, k_0), F_13(x, k_0)*F_15(x, k_0))
Eq(F_15(x, k_0), k_0*x)
Eq(F_16(x, k_0), F_17(x, k_0)*F_9(x))
Eq(F_17(x, k_0), (-k_0*F_18(x, k_0) + F_18(x, 1))/(1 - k_0))
Eq(F_18(x, k_0), F_1(x) + F_19(x, k_0) + F_20(x, k_0) + F_21(x, k_0) + F_6(x))
Eq(F_19(x, k_0), F_15(x, k_0)*F_18(x, k_0))
Eq(F_20(x, k_0), F_12(x, k_0)*F_9(x))
Eq(F_21(x, k_0), F_22(x, k_0)*F_9(x))
Eq(F_22(x, k_0), (-k_0*F_23(x, k_0) + F_23(x, 1))/(1 - k_0))
Eq(F_23(x, k_0), F_1(x) + F_24(x, k_0) + F_25(x, k_0) + F_50(x, k_0) + F_51(x, k_0))
Eq(F_24(x, k_0), F_15(x, k_0)*F_23(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0)*F_9(x))
Eq(F_26(x, k_0), (-k_0*F_27(x, k_0) + F_27(x, 1))/(1 - k_0))
Eq(F_27(x, k_0), F_1(x) + F_28(x, k_0) + F_29(x) + F_31(x) + F_51(x, k_0))
Eq(F_28(x, k_0), F_15(x, k_0)*F_27(x, k_0))
Eq(F_29(x), F_30(x)*F_9(x))
Eq(F_30(x), F_27(x, 1))
Eq(F_31(x), F_32(x)*F_9(x))
Eq(F_32(x), F_33(x, 1))
Eq(F_33(x, k_0), F_1(x) + F_34(x, k_0) + F_35(x) + F_37(x, k_0) + F_6(x))
Eq(F_34(x, k_0), F_15(x, k_0)*F_33(x, k_0))
Eq(F_35(x), F_36(x)*F_9(x))
Eq(F_36(x), F_13(x, 1))
Eq(F_37(x, k_0), F_38(x, k_0)*F_9(x))
Eq(F_38(x, k_0), F_1(x) + F_39(x, k_0) + F_40(x) + F_41(x) + F_42(x, k_0) + F_45(x, k_0))
Eq(F_39(x, k_0), F_15(x, k_0)*F_38(x, k_0))
Eq(F_40(x), F_24(x, 1))
Eq(F_41(x), F_25(x, 1))
Eq(F_42(x, k_0), F_43(x, k_0)*F_9(x))
Eq(F_43(x, k_0), (-k_0*F_44(x, k_0) + F_44(x, 1))/(1 - k_0))
Eq(F_44(x, k_0), (-k_0*F_33(x, k_0) + F_33(x, 1))/(1 - k_0))
Eq(F_45(x, k_0), F_46(x, k_0)*F_9(x))
Eq(F_46(x, k_0), (-k_0*F_47(x, k_0) + F_47(x, 1))/(1 - k_0))
Eq(F_47(x, k_0), (-k_0*F_48(x, k_0) + F_48(x, 1))/(1 - k_0))
Eq(F_48(x, k_0), F_1(x) + F_29(x) + F_49(x, k_0) + F_50(x, k_0) + F_51(x, k_0))
Eq(F_49(x, k_0), F_15(x, k_0)*F_48(x, k_0))
Eq(F_50(x, k_0), F_44(x, k_0)*F_9(x))
Eq(F_51(x, k_0), F_47(x, k_0)*F_9(x))
Eq(F_52(x), F_53(x)*F_9(x))
Eq(F_53(x), F_22(x, 1))
Eq(F_54(x), F_55(x)*F_9(x))
Eq(F_55(x), F_23(x, 1))
Eq(F_56(x), F_57(x)*F_9(x))
Eq(F_57(x), F_1(x) + F_29(x) + F_31(x) + F_58(x))
Eq(F_58(x), F_59(x)*F_9(x))
Eq(F_59(x), F_48(x, 1))
Pack JSON:
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Specification JSON:
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