The Series Expansion for 2D (2D site) Lattice-Animals of Locally Bounded Width The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (site) lattice animals of width <= 1 equals [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] The two last ratios (giving appx. to the "connective consts.") are: 1., 1. The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (site) lattice animals of width <= 2 equals [1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860, 33461, 80782, 195025, 470832, 1136689, 2744210, 6625109, 15994428, 38613965, 93222358, 225058681, 543339720, 1311738121, 3166815962, 7645370045, 18457556052, 44560482149, 107578520350, 259717522849, 627013566048, 1513744654945, 3654502875938, 8822750406821, 21300003689580, 51422757785981, 124145519261542, 299713796309065, 723573111879672, 1746860020068409, 4217293152016490, 10181446324101389, 24580185800219268, 59341817924539925, 143263821649299118, 345869461223138161, 835002744095575440, 2015874949414289041, 4866752642924153522, 11749380235262596085, 28365513113449345692, 68480406462161287469, 165326326037771920630, 399133058537705128729, 963592443113182178088, 2326317944764069484905, 5616228332641321147898, 13558774610046711780701, 32733777552734744709300, 79026329715516201199301, 190786436983767147107902, 460599203683050495415105, 1111984844349868137938112, 2684568892382786771291329, 6481122629115441680520770, 15646814150613670132332869, 37774750930342781945186508, 91196316011299234022705885, 220167382952941249990598278, 531531081917181734003902441, 1283229546787304717998403160, 3097990175491791170000708761, 7479209897770887057999820682, 18056409971033565286000350125, 43592029839838017630000520932, 105240469650709600546001391989, 254072969141257218722003304910, 613386407933224037990008001809, 1480845785007705294702019308528, 3575077977948634627394046618865, 8631001740904974549490112546258, 20837081459758583726374271711381, 50305164660422142002238655969020, 121447410780602867730851583649421, 293199986221627877463941823267862, 707847383223858622658735230185145, 1708894752669345122781412283638152, 4125636888562548868221559797461449, 9960168529794442859224531878561050, 24045973948151434586670623554583549, 58052116426097312032565778987728148, 140150206800346058651802181530039845, 338352530026789429336170142047807838, 816855266853924917324142465625655521, 1972063063734639263984455073299118880, 4760981394323203445293052612223893281, 11494025852381046154570560297746905442, 27749033099085295754434173207717704165, 66992092050551637663438906713182313772] The two last ratios (giving appx. to the "connective consts.") are: 2.414213562, 2.414213562 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (site) lattice animals of width <= 3 equals [1, 2, 6, 18, 54, 161, 482, 1443, 4317, 12916, 38641, 115606, 345865, 1034744, 3095710, 9261622, 27708575, 82897453, 248009449, 741985246, 2219843209, 6641242525, 19869016707, 59443368473, 177840408715, 532056170076, 1591785411808, 4762243047007, 14247497604650, 42625121393600, 127524216831077, 381522101210681, 1141423310242466, 3414866842668604, 10216468726804130, 30565242527658808, 91443929968038975, 273578471377484542, 818481664418913497, 2448702310590716225, 7325934430247062898, 21917451967990351793, 65571799112180139754, 196175214394794306029, 586909544406489031710, 1755893650368164879432, 5253215833320754146956, 15716371310794165329115, 47019641875748562365783, 140671576053005027368547, 420855870436621459628644, 1259100584856088100427671, 3766929236700965996970247, 11269755605692434999948259, 33716426147486566211308981, 100871521258607527859991073, 301783580398369815572492840, 902864636734998242812347916, 2701156077446497553047433417, 8081216007209379193934875476, 24177074660903460396546002052, 72332052334380244428984295693, 216400282841663420751344729349, 647418134874261464622546298090, 1936920949732551164585547669470, 5794806421728483814560833357530, 17336681432426217431850102355506, 51867224065058640042551681115577, 155174388056948411689011453981166, 464244831738927775782919065012527, 1388910028871576037418831344362057, 4155288193676375729297831130139940, 12431633160957466889533996750021317, 37192487222380545049849561711494266, 111271068561711142639692417404939481, 332896550446742254154607922873120448, 995947237065305690724254139513116918, 2979637060482863029118011773475263782, 8914364819529890418535836508369521039, 26669657586684193048423281673633060353, 79789267120042708215743027392518964529, 238710494383405629826801664842926033810, 714164977139589874600592832646137859193, 2136611613537199612192696022113607755841, 6392233353960375708555012311351935203307, 19124040603635007335029839827807758438449, 57214577246759803257607664654354309650615, 171172395905875229850348751562231607615380, 512107063096704411768267580871346895233976, 1532102432086893162696820103997951058531067, 4583685778931173301957324172191806487270730, 13713296761338399337743824372756704129551324, 41026919630687446303367304163046322524183297, 122742777588560556545520829065728959008360825, 367217173157837722468775287107377407525233234, 1098626370620775716784115455408964073206409184, 3286828586593885974830162552540430681013883634, 9833408742543127590831278363611051238428010408, 29419218237397900208611615896056887716329317647, 88015298088362701511458739292299924845054489638] The two last ratios (giving appx. to the "connective consts.") are: 2.991761962, 2.991761962 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (site) lattice animals of width <= 4 equals [1, 2, 6, 19, 62, 205, 678, 2242, 7411, 24470, 80751, 266423, 878915, 2899444, 9565000, 31554145, 104095235, 343405255, 1132878955, 3737321663, 12329274615, 40673780463, 134181164869, 442658243366, 1460311618335, 4817508874680, 15892766519386, 52429592475442, 172963100357646, 570598256903692, 1882380520286645, 6209897036124122, 20486198610053058, 67583138829316716, 222954035598448808, 735516326258955705, 2426438547043532037, 8004722413888767824, 26407254781387496209, 87116463136752122282, 287393680724666504082, 948100103544994472847, 3127743811470181291566, 10318300054616313173248, 34039653639997143740618, 112295437600947997220254, 370458096881781965808798, 1222126245528895684596604, 4031744946547059523482231, 13300563156609987077529549, 43878018730941568800125908, 144751805249393029163794460, 477530338173237965532142551, 1575353229501800593975981931, 5197026449032502863024997317, 17144779599991617553032978140, 56559932956856570426636717784, 186588926234180004447969388394, 615549304483461369373826926475, 2030672204922441166820606526391, 6699105293125000888613266264128, 22100076821650030978872546780217, 72907257633951546794613714382905, 240518087724299765686489521458627, 793459422284109928087372657409322, 2617590472168994580379682577833434, 8635324866728368705291902653782742, 28487586712579946682822712399787174, 93979393853913855100955241265847820, 310034210979649162015250192343753411, 1022790295149052570638734589075537025, 3374143726092707629362282540684683409, 11131163385424626356199374686746278653, 36721256819874272378582834001335685148, 121141937795725087204903490793614782011, 399642342441850346267578509929003492283, 1318403888682431495988797182952489664630, 4349360988809315307056215314210427594170, 14348365605839724576319932807062082227321, 47334676539508172965847332527969902675994, 156155179248287497390916596804103155666779, 515149606773211569134592794184799471729944, 1699457671760220099670037944651264293170581, 5606441973615140852815082402410876002705216, 18495424820412041920180304740625178064244581, 61015656792204989073327062326084473938627325, 201288178559459098141941197053107918619910045, 664041542087618738054152431972567621848071873, 2190646131202627403920708709986455517927933454, 7226852791568018068676325234277052750468004087, 23841094427388188941948451967158663500114841296, 78650804145176765770900841576362545258202451265, 259465814856915962708512455841907388799544095483, 855967206070733132473984476461073719844789401985, 2823801117201423177512477019097426319241147613866, 9315605426183913550134045306319813572797948292775, 30731804703849855390852857099200949010444686066754, 101382978040371371413012343507721018903617541531332, 334458335115178169043926215870650042267187135015891, 1103364490668961062182454330843836614873247372857039] The two last ratios (giving appx. to the "connective consts.") are: 3.298959466, 3.298959466 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (site) lattice animals of width <= 5 equals [1, 2, 6, 19, 63, 215, 747, 2610, 9128, 31912, 111452, 388832, 1355530, 4723343, 16453917, 57309912, 199602466, 695175588, 2421159855, 8432485263, 29369116619, 102288916893, 356260696840, 1240818329796, 4321643770770, 15051852230346, 52424102038548, 182587926708404, 635935536169909, 2214899927445436, 7714274797951745, 26868046349521987, 93578712355325706, 325925272451102511, 1135165040104909659, 3953665994255771965, 13770222160709933857, 47960302837686898148, 167040925141229522655, 581786790954160368867, 2026305050199685635853, 7057417289039043263757, 24580276691548405832837, 85610638780424366742556, 298173269750334806554611, 1038507597424828707515830, 3617017819238832644598605, 12597710346171057730067068, 43876561824360791842482594, 152817664847238071455025554, 532248601948833580411263433, 1853768506144234211498625325, 6456489809064061822673352274, 22487306541445663124135154460, 78321033633325210282004077262, 272784306030016347907480027136, 950080382808142209867952796808, 3309034698270200754355526520408, 11525036020628443563131219663831, 40140544717231081020008151948019, 139805491914477840023767823892436, 486928508497765116050046795557321, 1695923165399663842375997946741534, 5906730316145408702754417769935405, 20572549358065484547890300491924778, 71652126377462615295678203440931389, 249557170822831140900725438527408595, 869182600122873936912336353330239033, 3027275833691425889447574063195573423, 10543698150373203072350412181846294254, 36722643324716263152613488273653188164, 127901284115061161634875118525835837277, 445467346498755671792945231721717930592, 1551518095925627866447952082734422961288, 5403781940258128154076028475860175597829, 18820830601037118337571093861339938679963, 65551065610914462953439405293304190472041, 228307787993672846872080794378552560808820, 795173130639160497033135522029954138559424, 2769508273226345259165336311799852747480998, 9645919586472799839212166343547788888971195, 33595770616820737855996464261235378828687075, 117010700039513373234296537193435148976534983, 407536534282738247849632697712003141923423073, 1419408880718599703434438768628723599613655104, 4943658791741764619812891446509264203690372742, 17218267816383255191506738049810975546592296731, 59969500138630448907772654692952872345131817536, 208867755178907351899231814460079292759407439749, 727465445812073097200007436009322555082504185750, 2533689196770763562732046860621507354276788381325, 8824585391360642084456441448869865933126275113507, 30735145979493739769902045445470648977990594883447, 107047431294121905051529993350949836643355985838045, 372835468369508018510409821692953907909586704290373, 1298548548001855751386495759270612545348546605256653, 4522714372889407196425545880547929437623160004627423, 15752160618265303170283697607393974548452834156006866, 54863195790342653341183410571211448965880259261151474, 191083009199340104815523190300164481282248198576495104] The two last ratios (giving appx. to the "connective consts.") are: 3.482899719, 3.482899719 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (site) lattice animals of width <= 6 equals [1, 2, 6, 19, 63, 216, 759, 2710, 9756, 35251, 127532, 461353, 1667802, 6024080, 21742453, 78427041, 282770372, 1019236238, 3673129279, 13235830443, 47691574479, 171838748561, 619151765882, 2230866108236, 8038071257332, 28962265141682, 104355489543860, 376010291347368, 1354831734323659, 4881707947212571, 17589712041083337, 63379083719885943, 228366993779769574, 822850204288088967, 2964887697024754461, 10683061071427019536, 38493124219742155953, 138698126961488885562, 499756001001562676191, 1800716851258182633531, 6488328534843233086125, 23378693133075445738251, 84237918241433095295495, 303525385256566976105141, 1093660209309660738205857, 3940667602757293597260382, 14198981565811168757001345, 51161655293837837919067231, 184345261721765969969739670, 664231353183307569289025360, 2393353029628460258923713387, 8623710244732367253576521479, 31072882885514209247631455444, 111961559872403884293326405781, 403418985480617229507035336690, 1453596020240492656352092973983, 5237585404092911708194079945100, 18872025296812529913818377942519, 67999528661768177777930616674061, 245015350790205130485104721757515, 882837327025760902323133477503126, 3181032304609417072915394274573349, 11461869829457860743938667761417324, 41299316513366117033845865127436478, 148809362682377912412562491930515470, 536188690066056376492154072023710866, 1931990744213550653053679360901959325, 6961333397887196216604357876766859305, 25083020103319504731153529597687705799, 90378934830856040242775293796197694723, 325652645794397291546346981410784268182, 1173388975111991269327514406666359777013, 4227945649130879636940898391383720729402, 15234099511032833997794816879063127082528, 54891383941929326548114622020403202035513, 197784189927221856416956751243830292408127, 712654390833939650577347790977264718158337, 2567830527615867714498430356662831666075340, 9252386154304144073057594104769701092791576, 33338122834703429510055656565158267030492923, 120123654115403006701539834713009104841772971, 432828577349182501420121452364205832710866858, 1559564423424372728354471878809514595963490919, 5619409895961644117573099072637445607633907780, 20247812212525083229631892929006276629954621946, 72956752930286365733360489640160243415040311563, 262877181112845829422913856606792355239929269771, 947196929335225289078699171624040820177191112891, 3412932302240963882647442911678051324732414008445, 12297450022198487922798148349786424298999535452205, 44310072294481879340005237863174254358114232775991, 159657693521669227806886080233941652608622806684793, 575277307860174934349202705260173979893572826320623, 2072834535179689071078636676993429517454044118737622, 7468820604476069442799351678031599123346330628826645, 26911593894787439001670972976003262908712791789480232, 96967637102426410322542657991604008683327163763335765, 349393004442189331379610242665678724888562819171015968, 1258930043063667197883600760170308980403819406427059922, 4536166532179455144025375121511861061506331715560155225] The two last ratios (giving appx. to the "connective consts.") are: 3.603191899, 3.603191899 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (site) lattice animals of width <= 7 equals [1, 2, 6, 19, 63, 216, 760, 2724, 9893, 36247, 133526, 493338, 1825137, 6754195, 24988066, 92397782, 341452707, 1261113825, 4655519696, 17179642794, 63377121116, 233753542203, 862024117128, 3178614052761, 11720043016798, 43212037997001, 159320579095132, 587401876770568, 2165698221939737, 7984748504238142, 29439195457760058, 108540601880440248, 400184283555304881, 1475465756857005982, 5440004870944775604, 20057197074470101271, 73950612834932324225, 272655158824029789588, 1005277429060566938095, 3706451444027156436644, 13665665916962222720394, 50385240693950019058760, 185770136247462762319710, 684933593939901888979180, 2525346825730271985976338, 9310941268761862340447309, 34329393678004130769521748, 126572299280326823434298229, 466671412742153511490378331, 1720615059005957922767629921, 6343898654143063927746255255, 23389920706146062347354112766, 86238513137404080242521475857, 317960937637679940900570671022, 1172320277035043199352514782229, 4322338587045069655432459985124, 15936439224213218452480775683265, 58757566058818488393041946395995, 216638831313668844410492674974201, 798746210630025126231594891649681, 2944973000464920020452837380351961, 10858099680785801124096740035956874, 40033755377392206673354672224113668, 147604241710797479343887538130648770, 544216048873736720999583481063462276, 2006521658458279277008369000023070967, 7398034612183996757684676892294723662, 27276514008396703472847468680410071257, 100568361121652394814882415450748402755, 370795009059444301952016507124232426468, 1367119213351417491587594302981009072063, 5040561220780566185593833974489533548023, 18584522236514071981408669970360478669330, 68521033994349435588124586598218283101916, 252636685511811451380699131144448436154457, 931470106998264250119166370332667361948496, 3434325297899197940909648884570976228867250, 12662338987763821869641924251178978402700034, 46685976060277765642834175466331432144078171, 172130943801597804626142612470605875155212187, 634645868295877234877248194392308287018115464, 2339935918838298806883632155372340420053212468, 8627331205937572368800346297261609574958123919, 31808923969971439570819371643414835812381396586, 117279332388557094183616856626179336645479940911, 432408270662957465448529844585315393247095026759, 1594286979041217336040901073828540109806923825520, 5878127556726389442932263333204829820505585409830, 21672624833156036921333505692420338008688872565782, 79906851735676925610799913319834678897793459542990, 294616134568950717011760420801434285172611258571386, 1086248110931350077110090354259550877631554580549995, 4004990969786095205259738287220244186982694954205446, 14766380264924529739500356616187980121569869352791010, 54443564985116348078193458720071341819656301659956857, 200733132637075871194925963122262146771225387589108877, 740101985410202246765453009748499968070892738271391846, 2728752058079290661343664640076243434537757126528949389, 10060894229793168728183022939551228080772202879095826759, 37094463164356978131384999202830319217068707487791406410] The two last ratios (giving appx. to the "connective consts.") are: 3.686994647, 3.686994647