01342_01432_04132_40132
Counting sequence:
1, 1, 2, 6, 24, 116, 634, 3767, 23772, 157027, 1075196, 7578950, 54717750, 403054914, 3020006704, 22962542572, 176832394612, 1377042500685, 10829497000596, 85914994796005, 686953545471932, 5531473010122789, 44824440072307378, 365338078321603885, 2993362376118253488, 24644147348708094098, 203792181982164972554, 1692112505658159501907, 14102773460004136975720, 117948772089403003966732, 989665432536428796471382, 8328997982714159706310998, 70294154418278492013518246, 594824346449227337673122966, 5045794498157597210181959236, 42901878554127195257508119415, 365568938888411375771483589136, 3121431711529387196082894311417, 26704213827983880300412025291960, 228876404703262384071450528264386, 1965056227089561258133384668895140, 16899053618708452152740582548556427, 145554912376355197204399317524730050, 1255552031052653890849347709865359330, 10845625630856926067578477744744740636, 93811787592582099869698726095605595270, 812486149115037668097134965466924962948, 7045388190558120577953672440576261593932, 61164665218969250327596415040368765756350, 531594913751660469429452960862889407004904, 4625138926530841765597216273624909430370240, 40282182201452763851612967514551075804273909, 351177841699038643958282498318606121754624226, 3064431241116395504782868157138435764278107059, 26764865785044485948569509742285521158407731802, 233968478494352812010396769763168293656159740122, 2046973693915621118536942706409473396038390137640, 17923224116758089129306811993247890454747965581770, 157056547102960725059062849324928797795239892886864, 1377272104988182027086940713044415954420588030184909, 12086363582821849103806565530921377277850568211614454, 106138452676079889590894684858591644113484449733981074, 932697039644928033559330705651982951057987487736589080, 8201424070139459244676379678684207994676342805963027520, 72162126809731484353531655542126806084600039840262175578, 635318913361569679115147992700057240436504671002496779064, 5596649296752073511044130577588237639217877450553820840666, 49329884466628994926760843360320861100910044243551463915017, 435040833085001713866612366418536899656513542787878195279814, 3838667020221687923625128370725838037135295981364871362628089, 33888649922695006181302250065795232375860422926899283602016276, 299326194361416684942760277340062221129884667061415488425029873, 2645119707483462908080589294141538696935784261384991914108493676, 23385673819190053188016766564594691685019461854727841176744925788, 206848538365310911178851910890057517867683226114996668423582098268, 1830405651738071661059689346610459780881731064520182313268168961196, 16204256513803333349420848989131581881760916362327113715799266620466, 143513418614853850771471764432467736895733276245867652931915360876464, 1271547327379990067840089532237070359510879702754291034738891814093670, 11270530227448715383047220763715365757428221087221882678522265584499086, 99936315941087246092448909072066509428711195497709237266429929425705358, 886472037586547772706845963402740065833999221664671213399856865877211717, 7866203627968192654524795702632747251224090083173719282532326281195207776, 69826399452910533381718959145656709475824322507531702106887078508931936242, 620046798600988622425170546785152083584860491896043219307524298550143449082, 5507770438369050219480190129498929040719530325995553332911527970716972695119, 48940686298662475235395213490729357164460974246416978510748156081459377950442, 435014365433172520411921018638067887781823173791281384847515156829755463306627, 3867880469320538904157188864529323572749017558690281691100967864587793260464348, 34401319091544361630618770341142677009269585872555152375389977866771271747806762, 306059998060076600898157334860550914371461480629268109898299482113504184353598906, 2723732169296218081706140849618932074782435596233197717874118480137719168681976557, 24246307946629869117106305105751786684503105426325556237189637446110869851763231178, 215897371686364904245367104699003476752281223219769780604657813669843665729110591294, 1922944927756958734056869396662740194111847929620703373012913519273905943550242063532, 17131737543174102086417992385214674881901202462108781805699475929647301602652210253945, 152668157220183270631134472941673873269322173138228131386348590217945307694580387784266, 1360835073021090501807930643025338158283097450531257804747944652112754403260435324558431, 12133052547485282797489726621853096687309372541167480210666723149193409616912460117855544, 108203141341542131453822043869994784109749799658337820327609030013403477409153798539420063, 965189508232736944958406984393137240685692298282799903876798836870390463044700379801671172
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/24064/
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[4,x]
F[3,x] = x
F[4,x] = F[1,x]+F[5,x]+F[50,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[45,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[10,x,k[0]] = F[11,x,k[0]]*F[12,x,k[0]]
F[11,x,k[0]] = k[0]*x
F[12,x,k[0]] = F[13,x,k[0],1]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[0]*k[1]]
F[14,x,k[0],k[1]] = F[1,x]+F[15,x,k[0],k[1]]+F[17,x,k[0],k[1]]+F[19,x,k[1],k[0]]+F[20,x,k[0],k[1]]
F[15,x,k[0],k[1]] = F[16,x,k[0],k[1]]*F[3,x]
F[16,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[17,x,k[0],k[1]] = F[11,x,k[0]]*F[18,x,k[0],k[1]]
F[18,x,k[0],k[1]] = (F[13,x,k[0],1]*k[0]-F[13,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[19,x,k[0],k[1]] = F[11,x,k[0]]*F[14,x,k[1],k[0]]
F[20,x,k[0],k[1]] = F[21,x,k[0],k[1]]*F[3,x]
F[21,x,k[0],k[1]] = (F[22,x,k[0],k[1]]*k[1]-F[22,x,k[0],1])/(-1+k[1])
F[22,x,k[0],k[1]] = F[1,x]+F[23,x,k[0],k[1]]+F[25,x,k[0],k[1]]+F[42,x,k[1],k[0]]+F[44,x,k[0]]
F[23,x,k[0],k[1]] = F[24,x,k[0],k[1]]*F[3,x]
F[24,x,k[0],k[1]] = 1/(-1+k[0])*(F[22,x,k[0],k[1]]*k[0]-F[22,x,1,k[1]])
F[25,x,k[0],k[1]] = F[11,x,k[0]]*F[26,x,k[0],k[1]]
F[26,x,k[0],k[1]] = F[27,x,1,k[0],k[1]]
F[27,x,k[0],k[1],k[2]] = F[1,x]+F[28,x,k[0],k[1],k[2]]+F[30,x,k[0],k[1],k[2]]+F[41,x,k[1],k[0],k[2]]+F[42,x,k[2],k[0]*k[1]]+F[43,x,k[0],k[1]]
F[28,x,k[0],k[1],k[2]] = F[29,x,k[0],k[1],k[2]]*F[3,x]
F[29,x,k[0],k[1],k[2]] = 1/(k[0]*k[1]-1)*(F[27,x,k[0],k[1],k[2]]*k[0]*k[1]-F[27,x,1/k[1],k[1],k[2]])
F[30,x,k[0],k[1],k[2]] = F[31,x,k[0]*k[1],k[1],k[2]]
F[32,x,k[0],k[1],k[2]] = F[1,x]+F[31,x,k[0],k[1],k[2]]+F[33,x,k[0],k[1],k[2]]+F[35,x,k[1],k[0],k[2]]+F[37,x,k[2],k[0],k[1]]+F[38,x,k[0],k[1]]
F[32,x,k[0],k[1],k[2]] = (F[22,x,k[0],k[2]]*k[0]-F[22,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[33,x,k[0],k[1],k[2]] = F[3,x]*F[34,x,k[0],k[1],k[2]]
F[34,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[32,x,k[0],k[1],k[2]]*k[0]-F[32,x,1,k[1],k[2]])
F[35,x,k[0],k[1],k[2]] = F[11,x,k[0]]*F[36,x,k[1],k[0],k[2]]
F[36,x,k[0],k[1],k[2]] = (-F[27,x,1,k[1],k[2]]*k[1]+F[27,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[37,x,k[0],k[1],k[2]] = F[11,x,k[0]]*F[32,x,k[1],k[2],k[0]]
F[38,x,k[0],k[1]] = F[3,x]*F[39,x,k[0],k[1]]
F[39,x,k[0],k[1]] = (F[40,x,k[0]]*k[0]-F[40,x,k[1]]*k[1])/(-k[1]+k[0])
F[40,x,k[0]] = F[22,x,k[0],1]
F[41,x,k[0],k[1],k[2]] = F[11,x,k[0]]*F[27,x,k[1],k[0],k[2]]
F[42,x,k[0],k[1]] = F[11,x,k[0]]*F[22,x,k[1],k[0]]
F[43,x,k[0],k[1]] = F[20,x,k[0]*k[1],k[1]]
F[44,x,k[0]] = F[3,x]*F[40,x,k[0]]
F[45,x,k[0]] = F[3,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]] = F[1,x]+F[10,x,k[0]]+F[44,x,k[0]]+F[48,x,k[0]]
F[48,x,k[0]] = F[3,x]*F[49,x,k[0]]
F[49,x,k[0]] = 1/(-1+k[0])*(F[47,x,k[0]]*k[0]-F[47,x,1])
F[50,x] = F[3,x]*F[51,x]
F[51,x] = F[47,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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{50}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = \frac{y_{0} F_{7}\! \left(x , y_{0}\right)-F_{7}\! \left(x , 1\right)}{-1+y_{0}}
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right) F_{12}\! \left(x , y_{0}\right)
F_{11}\! \left(x , y_{0}\right) = y_{0} x
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}, 1\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}, y_{1}\right)+F_{17}\! \left(x , y_{0}, y_{1}\right)+F_{19}\! \left(x , y_{1}, y_{0}\right)+F_{20}\! \left(x , y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{14}\! \left(x , y_{0}, y_{1}\right)-F_{14}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{17}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}\right) F_{18}\! \left(x , y_{0}, y_{1}\right)
F_{18}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{13}\! \left(x , y_{0}, 1\right)-y_{1} F_{13}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{1}, y_{0}\right)
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{21}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{1} F_{22}\! \left(x , y_{0}, y_{1}\right)-F_{22}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{22}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{23}\! \left(x , y_{0}, y_{1}\right)+F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{42}\! \left(x , y_{1}, y_{0}\right)+F_{44}\! \left(x , y_{0}\right)
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{24}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{22}\! \left(x , y_{0}, y_{1}\right)-F_{22}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}\right) F_{26}\! \left(x , y_{0}, y_{1}\right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x , 1, y_{0}, y_{1}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{41}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{42}\! \left(x , y_{2}, y_{0} y_{1}\right)+F_{43}\! \left(x , y_{0}, y_{1}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{3}\! \left(x \right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} y_{1} F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{27}\! \left(x , \frac{1}{y_{1}}, y_{1}, y_{2}\right)}{y_{0} y_{1}-1}
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{31}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{35}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{37}\! \left(x , y_{2}, y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{0}, y_{1}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{22}\! \left(x , y_{0}, y_{2}\right)-y_{1} F_{22}\! \left(x , y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{3}\! \left(x \right) F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{32}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x , y_{0}\right) F_{36}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{-y_{1} F_{27}\! \left(x , 1, y_{1}, y_{2}\right)+y_{0} F_{27}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{1}, y_{2}, y_{0}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{39}\! \left(x , y_{0}, y_{1}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{40}\! \left(x , y_{0}\right)-y_{1} F_{40}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}
F_{40}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}, 1\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x , y_{0}\right) F_{27}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{1}, y_{0}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{44}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{40}\! \left(x , y_{0}\right)
F_{45}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{46}\! \left(x , y_{0}\right)
F_{46}\! \left(x , y_{0}\right) = \frac{y_{0} F_{47}\! \left(x , y_{0}\right)-F_{47}\! \left(x , 1\right)}{-1+y_{0}}
F_{47}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{44}\! \left(x , y_{0}\right)+F_{48}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{49}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = \frac{y_{0} F_{47}\! \left(x , y_{0}\right)-F_{47}\! \left(x , 1\right)}{-1+y_{0}}
F_{50}\! \left(x \right) = F_{3}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{47}\! \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_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_5(x) + F_50(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_10(x, k_0) + F_45(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_10(x, k_0), F_11(x, k_0)*F_12(x, k_0))
Eq(F_11(x, k_0), k_0*x)
Eq(F_12(x, k_0), F_13(x, k_0, 1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_0*k_1))
Eq(F_14(x, k_0, k_1), F_1(x) + F_15(x, k_0, k_1) + F_17(x, k_0, k_1) + F_19(x, k_1, k_0) + F_20(x, k_0, k_1))
Eq(F_15(x, k_0, k_1), F_16(x, k_0, k_1)*F_3(x))
Eq(F_16(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_17(x, k_0, k_1), F_11(x, k_0)*F_18(x, k_0, k_1))
Eq(F_18(x, k_0, k_1), (-k_0*F_13(x, k_0, 1) + k_1*F_13(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_19(x, k_0, k_1), F_11(x, k_0)*F_14(x, k_1, k_0))
Eq(F_20(x, k_0, k_1), F_21(x, k_0, k_1)*F_3(x))
Eq(F_21(x, k_0, k_1), (-k_1*F_22(x, k_0, k_1) + F_22(x, k_0, 1))/(1 - k_1))
Eq(F_22(x, k_0, k_1), F_1(x) + F_23(x, k_0, k_1) + F_25(x, k_0, k_1) + F_42(x, k_1, k_0) + F_44(x, k_0))
Eq(F_23(x, k_0, k_1), F_24(x, k_0, k_1)*F_3(x))
Eq(F_24(x, k_0, k_1), (k_0*F_22(x, k_0, k_1) - F_22(x, 1, k_1))/(k_0 - 1))
Eq(F_25(x, k_0, k_1), F_11(x, k_0)*F_26(x, k_0, k_1))
Eq(F_26(x, k_0, k_1), F_27(x, 1, k_0, k_1))
Eq(F_27(x, k_0, k_1, k_2), F_1(x) + F_28(x, k_0, k_1, k_2) + F_30(x, k_0, k_1, k_2) + F_41(x, k_1, k_0, k_2) + F_42(x, k_2, k_0*k_1) + F_43(x, k_0, k_1))
Eq(F_28(x, k_0, k_1, k_2), F_29(x, k_0, k_1, k_2)*F_3(x))
Eq(F_29(x, k_0, k_1, k_2), (k_0*k_1*F_27(x, k_0, k_1, k_2) - F_27(x, 1/k_1, k_1, k_2))/(k_0*k_1 - 1))
Eq(F_30(x, k_0, k_1, k_2), F_31(x, k_0*k_1, k_1, k_2))
Eq(F_32(x, k_0, k_1, k_2), F_1(x) + F_31(x, k_0, k_1, k_2) + F_33(x, k_0, k_1, k_2) + F_35(x, k_1, k_0, k_2) + F_37(x, k_2, k_0, k_1) + F_38(x, k_0, k_1))
Eq(F_32(x, k_0, k_1, k_2), (-k_0*F_22(x, k_0, k_2) + k_1*F_22(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_33(x, k_0, k_1, k_2), F_3(x)*F_34(x, k_0, k_1, k_2))
Eq(F_34(x, k_0, k_1, k_2), (k_0*F_32(x, k_0, k_1, k_2) - F_32(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_35(x, k_0, k_1, k_2), F_11(x, k_0)*F_36(x, k_1, k_0, k_2))
Eq(F_36(x, k_0, k_1, k_2), (-k_0*F_27(x, k_0/k_1, k_1, k_2) + k_1*F_27(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_37(x, k_0, k_1, k_2), F_11(x, k_0)*F_32(x, k_1, k_2, k_0))
Eq(F_38(x, k_0, k_1), F_3(x)*F_39(x, k_0, k_1))
Eq(F_39(x, k_0, k_1), (-k_0*F_40(x, k_0) + k_1*F_40(x, k_1))/(-k_0 + k_1))
Eq(F_40(x, k_0), F_22(x, k_0, 1))
Eq(F_41(x, k_0, k_1, k_2), F_11(x, k_0)*F_27(x, k_1, k_0, k_2))
Eq(F_42(x, k_0, k_1), F_11(x, k_0)*F_22(x, k_1, k_0))
Eq(F_43(x, k_0, k_1), F_20(x, k_0*k_1, k_1))
Eq(F_44(x, k_0), F_3(x)*F_40(x, k_0))
Eq(F_45(x, k_0), F_3(x)*F_46(x, k_0))
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), F_1(x) + F_10(x, k_0) + F_44(x, k_0) + F_48(x, k_0))
Eq(F_48(x, k_0), F_3(x)*F_49(x, k_0))
Eq(F_49(x, k_0), (k_0*F_47(x, k_0) - F_47(x, 1))/(k_0 - 1))
Eq(F_50(x), F_3(x)*F_51(x))
Eq(F_51(x), F_47(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "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": "col_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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 2, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 3]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 4]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 5]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[0, 6]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 5]]}, {"patt": [1, 0], "pos": [[1, 6], [1, 5]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 3], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 4], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 4], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 4], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 5], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 5], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 5], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 3], [1, 4], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 3], [1, 4], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 3], [1, 5], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 3], [1, 5], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 4], [1, 4], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 4], [1, 5], [1, 4]]}, {"patt": [1, 2, 0], "pos": [[1, 6], [1, 6], [1, 6]]}, {"patt": [2, 1, 0], "pos": [[1, 6], [1, 6], [1, 6]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 4], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 4], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 4], [1, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 4], [1, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 5], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 5], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 5], [1, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 5], [1, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 6], [1, 6], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 6], [1, 6], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 6], [1, 6], [1, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 3], [1, 6], [1, 6], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 3], [1, 6], [1, 6], [1, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 4], [1, 6], [1, 6], [1, 4]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 2], [1, 6], [1, 6], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 2], [1, 6], [1, 6], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 2], [1, 6], [1, 6], [1, 4]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 3], [1, 6], [1, 6], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 3], [1, 6], [1, 6], [1, 4]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 4], [1, 6], [1, 6], [1, 4]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 6], [1, 2], [1, 6], [1, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 6], [1, 2], [1, 6], [1, 3]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 6], [1, 2], [1, 6], [1, 4]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 6], [1, 3], [1, 6], [1, 3]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 6], [1, 3], [1, 6], [1, 4]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 6], [1, 4], [1, 6], [1, 4]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 6], [1, 6], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 6], [1, 6], [1, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 6], [1, 6], [1, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 6], [1, 6], [1, 4]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 6], [1, 6], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 6], [1, 6], [1, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 6], [1, 6], [1, 3]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 6], [1, 6], [1, 4]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 0], [1, 6], [1, 0], [1, 6], [1, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 0], [1, 6], [1, 0], [1, 6], [1, 2]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 0], [1, 6], [1, 0], [1, 6], [1, 3]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 0], [1, 6], [1, 0], [1, 6], [1, 4]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[1, 6], [1, 0], [1, 0], [1, 6], [1, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[1, 6], [1, 0], [1, 0], [1, 6], [1, 2]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[1, 6], [1, 0], [1, 0], [1, 6], [1, 3]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[1, 6], [1, 0], [1, 0], [1, 6], [1, 4]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 4]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 5]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[0, 6]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 4]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 5]]}, {"patt": [1, 0], "pos": [[1, 6], [1, 5]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 3], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 4], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 5], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 6], [1, 6], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 6], [1, 6], [1, 4]]}, {"patt": [1, 2, 0], "pos": [[1, 6], [1, 6], [1, 6]]}, {"patt": [2, 1, 0], "pos": [[1, 6], [1, 6], [1, 3]]}, {"patt": [2, 1, 0], "pos": [[1, 6], [1, 6], [1, 4]]}, {"patt": [2, 1, 0], "pos": [[1, 6], [1, 6], [1, 6]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 4], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 4], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 5], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 5], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 6], [1, 6], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 1], [1, 6], [1, 6], [1, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 6], [1, 1], [1, 6], [1, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 6], [1, 6], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 6], [1, 6], [1, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 6], [1, 6], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 6], [1, 6], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 0], [1, 6], [1, 0], [1, 6], [1, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 0], [1, 6], [1, 0], [1, 6], [1, 1]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[1, 6], [1, 0], [1, 0], [1, 6], [1, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[1, 6], [1, 0], [1, 0], [1, 6], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}, {"assumptions": 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