0132_1302_30241_420531
Counting sequence:
1, 1, 2, 6, 22, 87, 353, 1447, 5971, 24795, 103626, 435831, 1844051, 7845963, 33553795, 144169233, 622113535, 2695141249, 11718545059, 51124178941, 223734228330, 981964657716, 4321455087749, 19065862627305, 84314832161621, 373686674642073, 1659617316970834, 7385000956733269, 32921934614253250, 147016549596884630, 657583091600257626, 2945772787729038122, 13215257422562170770, 59367123643322539835, 267041665825159684625, 1202667393947188117460, 5422735213338557226711, 24477797177070015216274, 110607290359376284431921, 500300160930586288188948, 2265126280896088417185616, 10264784292318376654965957, 46556983792959056044246894, 211339436856584118907069194, 960110234004451264454551756, 4365073962778444660854682932, 19859946586465393722287609817, 90420591395332384446730505959, 411952378584666583926775152437, 1878042484422960327036346699907, 8567054355198621971890480699096, 39103438515578915821809721652200, 178585366355930743077672827404384, 816046674275181730631551681919067, 3730899516129387215337188025610894, 17066057638363021304938035886000460, 78102705899227833390031269546285360, 357605911977147361435270519703958597, 1638105758577199792752710767648685552, 7507080577672073049238793195147912260, 34418005515277243623072425094803938609, 157862764910787592407819909386699727720, 724348035180394065958519973440076121083, 3324933104701184505369987871119003705750, 15267970354561706507088093309271970894384, 70135426628431450282513171157632443425362, 322289765363721063795196027736816076074641, 1481507769266289420736368303431349917085433, 6812481165505700464846899763429117788967182, 31336209585693630634765429477513388325809150, 144186089892811142965692348616694914524839745, 663639418362578421808469573575748260918762699, 3055407973475355710559866779978621464702884112, 14071193442058515997959943045844303722592112015, 64820736826701912551964704549924478502695483244, 298686122785296414780018780835115118388113724040, 1376673828784096865389084607122753636339000367870, 6346861123985271752636404212865069075783827420514, 29268197596898999624866628862234955640685314848189, 135001697775112312913068553852645830742956914644037, 622853746417317963245290405971506509219736337193517, 2874312346848141053008085665298225031039133359400594, 13267234104733045618134647850534854042789678253584876, 61252383257530332313204953029788336478685171601173754, 282852131976163617109088700983403368277727542925895548, 1306434287042192862047562470642842030143679031373593776, 6035387935090845790272357066641506451828512483816534415, 27887542919658610457435901766601379250673139312133225389, 128884519908570470749534949773488270094552348796819097866, 595764720238720636773033632176092772626337738594944884546, 2754421877408758838089992578751252412530585143895669797695, 12736965977294136323919372277615949510298896501721236338518, 58908725653596898602343837020701995521041470430958663151790, 272501997895668959467339154600674107510081129877293138470536, 1260766164868542390882014952637834082362288652779379366458220, 5834083102630407997897022435245587609184603323421610188812336, 27001155995097546238050984039689823207503337363793429713973456, 124986268639600767376617159958840057693520525036237278094144520, 578643405714326860202848294226816357671451224084063877019450283, 2679335391315672544094077576324047526605371827332466579875081215, 12408210961802812481491199322235273119603424932216197258851320606
Implicit equation for the generating function in Maple syntax:
x^2*(x^4-6*x^3+12*x^2-8*x+2)*(x-1)^2*F(x)^4+x*(x-1)*(3*x^5-16*x^4+26*x^3-12*x^2+1)*F(x)^3+(3*x^7-22*x^6+67*x^5-112*x^4+109*x^3-57*x^2+14*x-1)*F(x)^2+x*(3*x^2-9*x+5)*(x-1)^3*F(x)+(x-1)^6 = 0
Implicit equation for the generating function in latex syntax:
x^{2} \left(x^{4}-6 x^{3}+12 x^{2}-8 x +2\right) \left(x -1\right)^{2} F \! \left(x \right)^{4}+x \left(x -1\right) \left(3 x^{5}-16 x^{4}+26 x^{3}-12 x^{2}+1\right) F \! \left(x \right)^{3}+\left(3 x^{7}-22 x^{6}+67 x^{5}-112 x^{4}+109 x^{3}-57 x^{2}+14 x -1\right) F \! \left(x \right)^{2}+x \left(3 x^{2}-9 x +5\right) \left(x -1\right)^{3} F \! \left(x \right)+\left(x -1\right)^{6} = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 22
a(5) = 87
a(6) = 353
a(7) = 1447
a(8) = 5971
a(9) = 24795
a(10) = 103626
a(11) = 435831
a(12) = 1844051
a(13) = 7845963
a(14) = 33553795
a(15) = 144169233
a(16) = 622113535
a(17) = 2695141249
a(18) = 11718545059
a(19) = 51124178941
a(20) = 223734228330
a(21) = 981964657716
a(22) = 4321455087749
a(23) = 19065862627305
a(24) = 84314832161621
a(25) = 373686674642073
a(26) = 1659617316970834
a(27) = 7385000956733269
a(28) = 32921934614253250
a(29) = 147016549596884630
a(30) = 657583091600257626
a(31) = 2945772787729038122
a(32) = 13215257422562170770
a(33) = 59367123643322539835
a(34) = 267041665825159684625
a(35) = 1202667393947188117460
a(36) = 5422735213338557226711
a(37) = 24477797177070015216274
a(38) = 110607290359376284431921
a(39) = 500300160930586288188948
a(40) = 2265126280896088417185616
a(41) = 10264784292318376654965957
a(42) = 46556983792959056044246894
a(43) = 211339436856584118907069194
a(44) = 960110234004451264454551756
a(45) = 4365073962778444660854682932
a(46) = 19859946586465393722287609817
a(47) = 90420591395332384446730505959
a(48) = 411952378584666583926775152437
a(49) = 1878042484422960327036346699907
a(50) = 8567054355198621971890480699096
a(51) = 39103438515578915821809721652200
a(52) = 178585366355930743077672827404384
a(53) = 816046674275181730631551681919067
a(n+54) = -1/2*(5257*n^2+546535*n+14205126)/(n+54)/(n+55)*a(n+52)-1/32*(44235685155961175137*n^3+4286241045974050624578*n^2+138417351189770619616529*n+1489753874582570149435038)/(n+55)/(n+54)/(n+53)*a(n+32)+1/32*(23288650489030052095*n^3+2324248672019727334206*n^2+77308189679437457554235*n+856984109372086729243416)/(n+55)/(n+54)/(n+53)*a(n+33)-1/32*(11169683584308834676*n^3+1147206790461797102475*n^2+39268253555824497965921*n+447960763583266301441520)/(n+55)/(n+54)/(n+53)*a(n+34)+3/32*(1623683299908221275*n^3+171481086289676412986*n^2+6035656913526794455417*n+70798736837128293131710)/(n+55)/(n+54)/(n+53)*a(n+35)-1/16*(963555294481623337*n^3+104563421858393757885*n^2+3781558889271530481269*n+45577328503601715772899)/(n+55)/(n+54)/(n+53)*a(n+36)+3/32*(229953362330413077*n^3+25622877999683997116*n^2+951478240678027904199*n+11774740957298859846264)/(n+55)/(n+54)/(n+53)*a(n+37)-3/32*(74264426761402485*n^3+8491295357915145440*n^2+323552962281704958605*n+4108598017367998552438)/(n+55)/(n+54)/(n+53)*a(n+38)+1/16*(32349724146038926*n^3+3793267709791417461*n^2+148228346202442159478*n+1930288516187455754271)/(n+55)/(n+54)/(n+53)*a(n+39)-3/16*(2805772201076593*n^3+337223481390591296*n^2+13506914541173188045*n+180287518105797439910)/(n+55)/(n+54)/(n+53)*a(n+40)+1/32*(3910081091629051*n^3+481480754696020038*n^2+19758108821544767561*n+270198715285399573974)/(n+55)/(n+54)/(n+53)*a(n+41)-3/8*(67307869977133*n^3+8488505971619997*n^2+356757707534111157*n+4996782712807793105)/(n+55)/(n+54)/(n+53)*a(n+42)+3/8*(12325422308298*n^3+1591588486378765*n^2+68492640868485408*n+982290039136649245)/(n+55)/(n+54)/(n+53)*a(n+43)-1/4*(2994663835645*n^3+395898728513376*n^2+17442810159804326*n+256120361437357041)/(n+55)/(n+54)/(n+53)*a(n+44)+1/16*(1715420844451*n^3+232168633561518*n^2+10472478182963093*n+157437414976983234)/(n+55)/(n+54)/(n+53)*a(n+45)-1/8*(108761973433*n^3+15069884614284*n^2+695945530222445*n+10712061329301774)/(n+55)/(n+54)/(n+53)*a(n+46)+3/4*(2040162804*n^3+289360368695*n^2+13679304782390*n+215546050985655)/(n+55)/(n+54)/(n+53)*a(n+47)-1/2*(305398838*n^3+44315899287*n^2+2143460964037*n+34556982803358)/(n+55)/(n+54)/(n+53)*a(n+48)+1/8*(106829729*n^3+15843554490*n^2+783219255955*n+12905792847330)/(n+55)/(n+54)/(n+53)*a(n+49)-1/2*(1985288*n^3+300489834*n^2+15160291183*n+254951229399)/(n+55)/(n+54)/(n+53)*a(n+50)+1/2*(118799*n^3+18323451*n^2+942043351*n+16143732471)/(n+55)/(n+54)/(n+53)*a(n+51)-3/16*(23203883*n^3+202484928*n^2+588455119*n+568166910)/(n+55)/(n+54)/(n+53)*a(n+2)+1/16*(1324937572*n^3+15463284279*n^2+60238448231*n+78216068430)/(n+55)/(n+54)/(n+53)*a(n+3)-3/16*(6250596270*n^3+91586737201*n^2+448090218863*n+731361920874)/(n+55)/(n+54)/(n+53)*a(n+4)-3/32*(30609458247009336*n^3+1179474471196475195*n^2+15151192493183126961*n+64881421932352872044)/(n+55)/(n+54)/(n+53)*a(n+12)+45/4*(2*n+3)*(6733*n^2+29174*n+31745)/(n+55)/(n+54)/(n+53)*a(n+1)+1/4*(299*n+15713)/(n+55)*a(n+53)+1/32*(175881031057546222627*n^3+15507272144766283538394*n^2+455697564046538503304663*n+4463170035667156803848406)/(n+55)/(n+54)/(n+53)*a(n+29)+3/16*(47200841046185098853*n^3+3886731601107341615681*n^2+106672460787446474888326*n+975784465326766158720499)/(n+55)/(n+54)/(n+53)*a(n+27)-1/32*(233208776068338660127*n^3+19882787689245840642393*n^2+564987418427153221920116*n+5350940285394945895955118)/(n+55)/(n+54)/(n+53)*a(n+28)-1/32*(315071456897315755981*n^3+25026290392857512744622*n^2+662552484953353047502913*n+5846305648080631466378028)/(n+55)/(n+54)/(n+53)*a(n+26)+1/32*(321133674564010395859*n^3+24571738712191282768497*n^2+626650492261529570584736*n+5326666690256543055900786)/(n+55)/(n+54)/(n+53)*a(n+25)-1/32*(299808765606580917355*n^3+22065929402054315895303*n^2+541305338830982380747298*n+4425943976606642723179548)/(n+55)/(n+54)/(n+53)*a(n+24)+1/32*(256267731295763700950*n^3+18114010690732069202529*n^2+426756315247947826485697*n+3351130946258492568754284)/(n+55)/(n+54)/(n+53)*a(n+23)-1/32*(200419363462759988680*n^3+13581921029947930580685*n^2+306781823333772055462655*n+2309651924994689992329042)/(n+55)/(n+54)/(n+53)*a(n+22)+1/32*(143278244089151702828*n^3+9291712442733592456719*n^2+200844689755634497290493*n+1447023935497251109682070)/(n+55)/(n+54)/(n+53)*a(n+21)-1/32*(93520040775090004487*n^3+5792057310522084794370*n^2+119567281731331387626211*n+822706540059653625218544)/(n+55)/(n+54)/(n+53)*a(n+20)+1/32*(55652891570641606763*n^3+3284437500949912518498*n^2+64608277647596395237603*n+423614631915943390881564)/(n+55)/(n+54)/(n+53)*a(n+19)-1/32*(30142788557254728176*n^3+1690961374957876123995*n^2+31618478613140792355547*n+197063810617776569926398)/(n+55)/(n+54)/(n+53)*a(n+18)+1/32*(14829162396779514683*n^3+788601262542672623982*n^2+13978463466306045738985*n+82589303914440001603242)/(n+55)/(n+54)/(n+53)*a(n+17)-3/32*(2203691076241577861*n^3+110752963594804705264*n^2+1855353809921615708805*n+10360137398153020419904)/(n+55)/(n+54)/(n+53)*a(n+16)+1/32*(2663665586922502229*n^3+126082020308139550056*n^2+1989304526382609106111*n+10462213239504012945888)/(n+55)/(n+54)/(n+53)*a(n+15)-1/32*(966935019386040212*n^3+42937921271882592405*n^2+635580673468158514207*n+3136057078520578900446)/(n+55)/(n+54)/(n+53)*a(n+14)+3/16*(52521158789046874*n^3+2178214482752605915*n^2+30114046809731598135*n+138782399918323398726)/(n+55)/(n+54)/(n+53)*a(n+13)+1/32*(23813975655058906*n^3+847400472583644105*n^2+10053192868340213411*n+39761282732580601410)/(n+55)/(n+54)/(n+53)*a(n+11)-3/32*(1822032705140176*n^3+59443321480904427*n^2+646629169119787005*n+2345222893178734050)/(n+55)/(n+54)/(n+53)*a(n+10)+1/32*(1103352622216432*n^3+32717841148928685*n^2+323537942752741217*n+1066817992655540952)/(n+55)/(n+54)/(n+53)*a(n+9)-3/32*(64781683137051*n^3+1727628694915868*n^2+15367616254679701*n+45587864526331896)/(n+55)/(n+54)/(n+53)*a(n+8)+1/16*(14792824561088*n^3+350166843351279*n^2+2765476270430233*n+7284948622036656)/(n+55)/(n+54)/(n+53)*a(n+7)-1/8*(961176520459*n^3+19862557320363*n^2+136985056966376*n+315174453370476)/(n+55)/(n+54)/(n+53)*a(n+6)+1/16*(209713891603*n^3+3702519650433*n^2+21822813126368*n+42915570066144)/(n+55)/(n+54)/(n+53)*a(n+5)+1/32*(76670900390438371655*n^3+7206155093606574993615*n^2+225731410990225347544174*n+2356654329853091249558232)/(n+55)/(n+54)/(n+53)*a(n+31)-1/16*(60710555628696931154*n^3+5529477356823724603923*n^2+167851123960823807655163*n+1698185250358751335682811)/(n+55)/(n+54)/(n+53)*a(n+30)-2625/4*(2*n+3)*(2*n+1)*(n+1)/(n+55)/(n+54)/(n+53)*a(n), n >= 54
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 22
a \! \left(5\right) = 87
a \! \left(6\right) = 353
a \! \left(7\right) = 1447
a \! \left(8\right) = 5971
a \! \left(9\right) = 24795
a \! \left(10\right) = 103626
a \! \left(11\right) = 435831
a \! \left(12\right) = 1844051
a \! \left(13\right) = 7845963
a \! \left(14\right) = 33553795
a \! \left(15\right) = 144169233
a \! \left(16\right) = 622113535
a \! \left(17\right) = 2695141249
a \! \left(18\right) = 11718545059
a \! \left(19\right) = 51124178941
a \! \left(20\right) = 223734228330
a \! \left(21\right) = 981964657716
a \! \left(22\right) = 4321455087749
a \! \left(23\right) = 19065862627305
a \! \left(24\right) = 84314832161621
a \! \left(25\right) = 373686674642073
a \! \left(26\right) = 1659617316970834
a \! \left(27\right) = 7385000956733269
a \! \left(28\right) = 32921934614253250
a \! \left(29\right) = 147016549596884630
a \! \left(30\right) = 657583091600257626
a \! \left(31\right) = 2945772787729038122
a \! \left(32\right) = 13215257422562170770
a \! \left(33\right) = 59367123643322539835
a \! \left(34\right) = 267041665825159684625
a \! \left(35\right) = 1202667393947188117460
a \! \left(36\right) = 5422735213338557226711
a \! \left(37\right) = 24477797177070015216274
a \! \left(38\right) = 110607290359376284431921
a \! \left(39\right) = 500300160930586288188948
a \! \left(40\right) = 2265126280896088417185616
a \! \left(41\right) = 10264784292318376654965957
a \! \left(42\right) = 46556983792959056044246894
a \! \left(43\right) = 211339436856584118907069194
a \! \left(44\right) = 960110234004451264454551756
a \! \left(45\right) = 4365073962778444660854682932
a \! \left(46\right) = 19859946586465393722287609817
a \! \left(47\right) = 90420591395332384446730505959
a \! \left(48\right) = 411952378584666583926775152437
a \! \left(49\right) = 1878042484422960327036346699907
a \! \left(50\right) = 8567054355198621971890480699096
a \! \left(51\right) = 39103438515578915821809721652200
a \! \left(52\right) = 178585366355930743077672827404384
a \! \left(53\right) = 816046674275181730631551681919067
a \! \left(n +54\right) = \frac{\left(299 n +15713\right) a \! \left(n +53\right)}{4 n +220}-\frac{\left(5257 n^{2}+546535 n +14205126\right) a \! \left(n +52\right)}{2 \left(n +54\right) \left(n +55\right)}-\frac{\left(44235685155961175137 n^{3}+4286241045974050624578 n^{2}+138417351189770619616529 n +1489753874582570149435038\right) a \! \left(n +32\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(23288650489030052095 n^{3}+2324248672019727334206 n^{2}+77308189679437457554235 n +856984109372086729243416\right) a \! \left(n +33\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{\left(11169683584308834676 n^{3}+1147206790461797102475 n^{2}+39268253555824497965921 n +447960763583266301441520\right) a \! \left(n +34\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{3 \left(1623683299908221275 n^{3}+171481086289676412986 n^{2}+6035656913526794455417 n +70798736837128293131710\right) a \! \left(n +35\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{\left(963555294481623337 n^{3}+104563421858393757885 n^{2}+3781558889271530481269 n +45577328503601715772899\right) a \! \left(n +36\right)}{16 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{3 \left(229953362330413077 n^{3}+25622877999683997116 n^{2}+951478240678027904199 n +11774740957298859846264\right) a \! \left(n +37\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{3 \left(74264426761402485 n^{3}+8491295357915145440 n^{2}+323552962281704958605 n +4108598017367998552438\right) a \! \left(n +38\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(32349724146038926 n^{3}+3793267709791417461 n^{2}+148228346202442159478 n +1930288516187455754271\right) a \! \left(n +39\right)}{16 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{3 \left(2805772201076593 n^{3}+337223481390591296 n^{2}+13506914541173188045 n +180287518105797439910\right) a \! \left(n +40\right)}{16 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(3910081091629051 n^{3}+481480754696020038 n^{2}+19758108821544767561 n +270198715285399573974\right) a \! \left(n +41\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{3 \left(67307869977133 n^{3}+8488505971619997 n^{2}+356757707534111157 n +4996782712807793105\right) a \! \left(n +42\right)}{8 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{3 \left(12325422308298 n^{3}+1591588486378765 n^{2}+68492640868485408 n +982290039136649245\right) a \! \left(n +43\right)}{8 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{\left(2994663835645 n^{3}+395898728513376 n^{2}+17442810159804326 n +256120361437357041\right) a \! \left(n +44\right)}{4 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(1715420844451 n^{3}+232168633561518 n^{2}+10472478182963093 n +157437414976983234\right) a \! \left(n +45\right)}{16 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{\left(108761973433 n^{3}+15069884614284 n^{2}+695945530222445 n +10712061329301774\right) a \! \left(n +46\right)}{8 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{3 \left(2040162804 n^{3}+289360368695 n^{2}+13679304782390 n +215546050985655\right) a \! \left(n +47\right)}{4 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{\left(305398838 n^{3}+44315899287 n^{2}+2143460964037 n +34556982803358\right) a \! \left(n +48\right)}{2 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(106829729 n^{3}+15843554490 n^{2}+783219255955 n +12905792847330\right) a \! \left(n +49\right)}{8 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{\left(1985288 n^{3}+300489834 n^{2}+15160291183 n +254951229399\right) a \! \left(n +50\right)}{2 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(118799 n^{3}+18323451 n^{2}+942043351 n +16143732471\right) a \! \left(n +51\right)}{2 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{3 \left(23203883 n^{3}+202484928 n^{2}+588455119 n +568166910\right) a \! \left(n +2\right)}{16 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(1324937572 n^{3}+15463284279 n^{2}+60238448231 n +78216068430\right) a \! \left(n +3\right)}{16 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{3 \left(6250596270 n^{3}+91586737201 n^{2}+448090218863 n +731361920874\right) a \! \left(n +4\right)}{16 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{3 \left(30609458247009336 n^{3}+1179474471196475195 n^{2}+15151192493183126961 n +64881421932352872044\right) a \! \left(n +12\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{45 \left(2 n +3\right) \left(6733 n^{2}+29174 n +31745\right) a \! \left(n +1\right)}{4 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(175881031057546222627 n^{3}+15507272144766283538394 n^{2}+455697564046538503304663 n +4463170035667156803848406\right) a \! \left(n +29\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{3 \left(47200841046185098853 n^{3}+3886731601107341615681 n^{2}+106672460787446474888326 n +975784465326766158720499\right) a \! \left(n +27\right)}{16 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{\left(233208776068338660127 n^{3}+19882787689245840642393 n^{2}+564987418427153221920116 n +5350940285394945895955118\right) a \! \left(n +28\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{\left(315071456897315755981 n^{3}+25026290392857512744622 n^{2}+662552484953353047502913 n +5846305648080631466378028\right) a \! \left(n +26\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(321133674564010395859 n^{3}+24571738712191282768497 n^{2}+626650492261529570584736 n +5326666690256543055900786\right) a \! \left(n +25\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{\left(299808765606580917355 n^{3}+22065929402054315895303 n^{2}+541305338830982380747298 n +4425943976606642723179548\right) a \! \left(n +24\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(256267731295763700950 n^{3}+18114010690732069202529 n^{2}+426756315247947826485697 n +3351130946258492568754284\right) a \! \left(n +23\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{\left(200419363462759988680 n^{3}+13581921029947930580685 n^{2}+306781823333772055462655 n +2309651924994689992329042\right) a \! \left(n +22\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(143278244089151702828 n^{3}+9291712442733592456719 n^{2}+200844689755634497290493 n +1447023935497251109682070\right) a \! \left(n +21\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{\left(93520040775090004487 n^{3}+5792057310522084794370 n^{2}+119567281731331387626211 n +822706540059653625218544\right) a \! \left(n +20\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(55652891570641606763 n^{3}+3284437500949912518498 n^{2}+64608277647596395237603 n +423614631915943390881564\right) a \! \left(n +19\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{\left(30142788557254728176 n^{3}+1690961374957876123995 n^{2}+31618478613140792355547 n +197063810617776569926398\right) a \! \left(n +18\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(14829162396779514683 n^{3}+788601262542672623982 n^{2}+13978463466306045738985 n +82589303914440001603242\right) a \! \left(n +17\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{3 \left(2203691076241577861 n^{3}+110752963594804705264 n^{2}+1855353809921615708805 n +10360137398153020419904\right) a \! \left(n +16\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(2663665586922502229 n^{3}+126082020308139550056 n^{2}+1989304526382609106111 n +10462213239504012945888\right) a \! \left(n +15\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{\left(966935019386040212 n^{3}+42937921271882592405 n^{2}+635580673468158514207 n +3136057078520578900446\right) a \! \left(n +14\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{3 \left(52521158789046874 n^{3}+2178214482752605915 n^{2}+30114046809731598135 n +138782399918323398726\right) a \! \left(n +13\right)}{16 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(23813975655058906 n^{3}+847400472583644105 n^{2}+10053192868340213411 n +39761282732580601410\right) a \! \left(n +11\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{3 \left(1822032705140176 n^{3}+59443321480904427 n^{2}+646629169119787005 n +2345222893178734050\right) a \! \left(n +10\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(1103352622216432 n^{3}+32717841148928685 n^{2}+323537942752741217 n +1066817992655540952\right) a \! \left(n +9\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{3 \left(64781683137051 n^{3}+1727628694915868 n^{2}+15367616254679701 n +45587864526331896\right) a \! \left(n +8\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(14792824561088 n^{3}+350166843351279 n^{2}+2765476270430233 n +7284948622036656\right) a \! \left(n +7\right)}{16 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{\left(961176520459 n^{3}+19862557320363 n^{2}+136985056966376 n +315174453370476\right) a \! \left(n +6\right)}{8 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(209713891603 n^{3}+3702519650433 n^{2}+21822813126368 n +42915570066144\right) a \! \left(n +5\right)}{16 \left(n +55\right) \left(n +54\right) \left(n +53\right)}+\frac{\left(76670900390438371655 n^{3}+7206155093606574993615 n^{2}+225731410990225347544174 n +2356654329853091249558232\right) a \! \left(n +31\right)}{32 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{\left(60710555628696931154 n^{3}+5529477356823724603923 n^{2}+167851123960823807655163 n +1698185250358751335682811\right) a \! \left(n +30\right)}{16 \left(n +55\right) \left(n +54\right) \left(n +53\right)}-\frac{2625 \left(2 n +3\right) \left(2 n +1\right) \left(n +1\right) a \! \left(n \right)}{4 \left(n +55\right) \left(n +54\right) \left(n +53\right)}, \quad n \geq 54
Specification 1
Strategy pack name: insertion_row_and_col_placements_req_corrob_expand_verified
Tree: http://permpal.com/tree/24038/
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[3,x] = F[4,x]*F[8,x]
F[4,x] = F[5,x]+F[9,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[5,x]^2*F[8,x]
F[8,x] = x
F[9,x] = F[10,x]+F[2,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[8,x]
F[12,x] = F[13,x]+F[20,x]
F[13,x] = F[14,x]+F[9,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[19,x]*F[5,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[8,x]
F[18,x] = F[1,x]+F[16,x]
F[19,x] = F[6,x]
F[20,x] = F[21,x]+F[37,x]
F[21,x] = F[22,x]*F[5,x]
F[22,x] = F[2,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[8,x]
F[25,x] = F[26,x]+F[34,x]
F[26,x] = F[15,x]+F[27,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[2,x]*F[29,x]
F[29,x] = F[1,x]+F[30,x]
F[30,x] = F[29,x]*F[8,x]
F[31,x] = F[16,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[19,x]*F[29,x]*F[5,x]*F[8,x]
F[34,x] = F[21,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[2,x]*F[26,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[2,x]*F[9,x]
F[39,x] = F[40,x]
F[40,x] = F[16,x]*F[23,x]*F[5,x]
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_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \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_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{5} \left(x \right)^{2} F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{2}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{20}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{5}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{8}\! \left(x \right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{19}\! \left(x \right) = F_{6}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{37}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{5}\! \left(x \right)
F_{22}\! \left(x \right) = F_{2}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{8}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{34}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{2}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{29}\! \left(x \right) F_{8}\! \left(x \right)
F_{31}\! \left(x \right) = F_{16}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{19}\! \left(x \right) F_{29}\! \left(x \right) F_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{34}\! \left(x \right) = F_{21}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right) F_{26}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right) F_{9}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \left(x \right) F_{23}\! \left(x \right) F_{5}\! \left(x \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))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_5(x) + F_9(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_5(x)**2*F_8(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x) + F_2(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_8(x))
Eq(F_12(x), F_13(x) + F_20(x))
Eq(F_13(x), F_14(x) + F_9(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_19(x)*F_5(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_8(x))
Eq(F_18(x), F_1(x) + F_16(x))
Eq(F_19(x), F_6(x))
Eq(F_20(x), F_21(x) + F_37(x))
Eq(F_21(x), F_22(x)*F_5(x))
Eq(F_22(x), F_2(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_8(x))
Eq(F_25(x), F_26(x) + F_34(x))
Eq(F_26(x), F_15(x) + F_27(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_2(x)*F_29(x))
Eq(F_29(x), F_1(x) + F_30(x))
Eq(F_30(x), F_29(x)*F_8(x))
Eq(F_31(x), F_16(x)*F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_19(x)*F_29(x)*F_5(x)*F_8(x))
Eq(F_34(x), F_21(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_2(x)*F_26(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_2(x)*F_9(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_16(x)*F_23(x)*F_5(x))
Pack JSON:
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Specification JSON:
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"comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "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": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: insertion_point_placements_expand_verified
Tree: http://permpal.com/tree/24039/
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[3,x] = F[4,x]*F[8,x]
F[4,x] = F[5,x]+F[9,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[5,x]^2*F[8,x]
F[8,x] = x
F[9,x] = F[10,x]+F[2,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[8,x]
F[12,x] = F[13,x]+F[20,x]
F[13,x] = F[14,x]+F[9,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[19,x]*F[5,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[8,x]
F[18,x] = F[1,x]+F[16,x]
F[19,x] = F[6,x]
F[20,x] = F[21,x]+F[37,x]
F[21,x] = F[22,x]*F[5,x]
F[22,x] = F[2,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[8,x]
F[25,x] = F[26,x]+F[34,x]
F[26,x] = F[15,x]+F[27,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[2,x]*F[29,x]
F[29,x] = F[1,x]+F[30,x]
F[30,x] = F[29,x]*F[8,x]
F[31,x] = F[16,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[19,x]*F[29,x]*F[5,x]*F[8,x]
F[34,x] = F[21,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[2,x]*F[26,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[2,x]*F[9,x]
F[39,x] = F[40,x]
F[40,x] = F[16,x]*F[23,x]*F[5,x]
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_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \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_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{5} \left(x \right)^{2} F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{2}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{20}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{5}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{8}\! \left(x \right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{19}\! \left(x \right) = F_{6}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{37}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{5}\! \left(x \right)
F_{22}\! \left(x \right) = F_{2}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{8}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{34}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{2}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{29}\! \left(x \right) F_{8}\! \left(x \right)
F_{31}\! \left(x \right) = F_{16}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{19}\! \left(x \right) F_{29}\! \left(x \right) F_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{34}\! \left(x \right) = F_{21}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right) F_{26}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right) F_{9}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \left(x \right) F_{23}\! \left(x \right) F_{5}\! \left(x \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))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_5(x) + F_9(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_5(x)**2*F_8(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x) + F_2(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_8(x))
Eq(F_12(x), F_13(x) + F_20(x))
Eq(F_13(x), F_14(x) + F_9(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_19(x)*F_5(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_8(x))
Eq(F_18(x), F_1(x) + F_16(x))
Eq(F_19(x), F_6(x))
Eq(F_20(x), F_21(x) + F_37(x))
Eq(F_21(x), F_22(x)*F_5(x))
Eq(F_22(x), F_2(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_8(x))
Eq(F_25(x), F_26(x) + F_34(x))
Eq(F_26(x), F_15(x) + F_27(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_2(x)*F_29(x))
Eq(F_29(x), F_1(x) + F_30(x))
Eq(F_30(x), F_29(x)*F_8(x))
Eq(F_31(x), F_16(x)*F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_19(x)*F_29(x)*F_5(x)*F_8(x))
Eq(F_34(x), F_21(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_2(x)*F_26(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_2(x)*F_9(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_16(x)*F_23(x)*F_5(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_point_placements_expand_verified", "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, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 2, 0, 5, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 2, 0, 5, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 2, 0, 5, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], 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