The Series Expansion for 2D (2D site) Lattice-Animals of Globally 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, 10, 19, 36, 67, 124, 229, 422, 777, 1430, 2631, 4840, 8903, 16376, 30121, 55402, 101901, 187426, 344731, 634060, 1166219, 2145012, 3945293, 7256526, 13346833, 24548654, 45152015, 83047504, 152748175, 280947696, 516743377, 950439250, 1748130325, 3215312954, 5913882531, 10877325812, 20006521299, 36797729644, 67681576757, 124485827702, 228965134105, 421132538566, 774583500375, 1424681173048, 2620397211991, 4819661885416, 8864740270457, 16304799367866, 29989201523741, 55158741162066, 101452742053675, 186600684739484, 343212167955227, 631265594748388, 1161078447443101, 2135556210146718, 3927900252338209, 7224534909928030, 13287991372412959, 24440426534679200, 44952952817020191, 82681370724112352, 152074750075811745, 279709073616944290, 514465194416868389, 946249018109624426, 1740423286143437107, 3201137498669929924, 5887809802922991459, 10829370587736358492, 19918317889329279877, 36635498279988629830, 67383186757054268201, 123937002926372177910, 227955687963415075943, 419275877646841522056, 771168568536628775911, 1418400134146885373912, 2608844580330355671881, 4798413283013869821706, 8825657997491110867501, 16232915860835336361090, 29856987141340317050299, 54915560999666764278892, 101005464001842417690283, 185778012142849499019476, 341699037144358680988653, 628482513289050597698414, 1155959562576258777706545, 2126141113009668056393614, 3910583188874977431798575, 7192683864460904265898736, 13229408166345549754090927, 24332675219681431451788240, 44754767250487885471777905, 82316850636514866677657074, 151404293106684183601223221, 278475910993686935750658202 The two last ratios (giving appx. to the "connective consts.") are: 1.839286755, 1.839286755 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, 50, 131, 336, 845, 2095, 5150, 12581, 30592, 74133, 179182, 432244, 1041162, 2505055, 6022027, 14467157, 34738100, 83380127, 200074493, 479980295, 1151278523, 2761087429, 6621189768, 15876627968, 38067530229, 91270692828, 218822923582, 524617342479, 1257718761839, 3015210138514, 7228469851732, 17328905403858, 41542515856744, 99589163419141, 238742398725790, 572328832093609, 1372020576649641, 3289082765804884, 7884757639021465, 18901723717589268, 45312090781106211, 108624179165372160, 260398629931371880, 624238735773862296, 1496451359405018007, 3587355339392674791, 8599755685262390405, 20615685079775067502, 49420756032111858219, 118473430539237984423, 284009271043599057197, 680838411868253998877, 1632133080985759917001, 3912614615843252005694, 9379475846489796529908, 22484853321461702139603, 53901585858996356933232, 129215027071005382313614, 309759403803235256705983, 742567562651091549759661, 1780112487222550300804404, 4267356421361491155589128, 10229876432993637184889004, 24523466356930713490138570, 58788628113735414169862007, 140930435415003268851817044, 337844039675831966750767857, 809893155669453221604756027, 1941508051741629727415149252, 4654260240509479605312349009, 11157377565552672922333818372, 26746908784329373924744195247, 64118752384852958941250926178, 153708020615739852429934860878, 368474973707007407940512924502, 883322846092056851560229281951, 2117536620005294448919243000459, 5076242912417643152859990124083, 12168971181651110882121240162354, 29171941171980903389739139339529, 69932136334295339049624172297399, 167644095515164266637567410114977, 401883086002070288174503001968683, 963410099930300220995974216756727, 2309524966263594243417929876185658, 5536485002752674363332376734354568, 13272281803977352014363337875110179, 31816841226160274544543975994313012, 76272595817301913145446198356696936, 182843696875691426789232380597542229, 438320174223511467324553744518179393, 1050758535372018567296207218342462798, 2518920105861156631107928024566918864, 6038455350220719840686468458114899194, 14475625063195235748556547657962785428, 34701543493645708910291232385625409085, 83187918696701091954105711968913053052 The two last ratios (giving appx. to the "connective consts.") are: 2.397239728, 2.397239728 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, 199, 618, 1872, 5563, 16282, 47139, 135377, 386367, 1097250, 3103584, 8749435, 24597577, 68990933, 193124079, 539704199, 1506118087, 4197950609, 11688733557, 32517281820, 90392522483, 251112802794, 697208926226, 1934855759022, 5367286283750, 14883539567410, 41259528591079, 114347622854006, 316833125396052, 877704080915436, 2431036117347990, 6732409415305973, 18642069313703877, 51614259704375122, 142890627502761671, 395550404747671720, 1094885758191721412, 3030462011919462979, 8387365369517892666, 23212509177524758610, 64239348885888100070, 177772684580652457886, 491944169635953334092, 1361304396282636476632, 3766906484010009049915, 10423316111934359373281, 28841616499106208395318, 79804410225605841501576, 220815038607152988587247, 610978044627718131966619, 1690512566658834504489551, 4677433277595123567856842, 12941770032467947512996962, 35807751614921813931205818, 99073631939664971671820557, 274117704690962179756279545, 758427952708462783060598502, 2098408574471665151193919377, 5805831850664974119079806483, 16063408784067196755045868833, 44443676593383264223455253450, 122964964133738407903069423604, 340213899235756741282023276278, 941287026798839669479300210972, 2604303144940262221088973408398, 7205440128938478501816905852381, 19935589082262379724409740498379, 55156572339795756450784192372857, 152603730717131535467821443022311, 422214126458832091626619280020822, 1168154086255510559590850938852607, 3231969847979889842543081065943081, 8941992289885811084099284686161786, 24740081616495652229081951798204910, 68449114124275611285739651731637933, 189380134329788469634775360785760146, 523963348294988970507076626807438979, 1449663855086208169056920048778462070, 4010824299964602712633182128624384141, 11096854695253206153347045244047786032, 30701960231808443584577508783663537527, 84943912668873108797187580466980031555, 235016511726050562682163019788500959157, 650226183231730440613237873411882585071, 1798997250638424735292117817570183643658, 4977330944605450003784961720073938655857, 13770905966414847701931104163434431673502, 38100308022084635073429353740907313147805, 105413065422326408622887178113640261002207, 291648927314851761716892019822649733237581, 806912253541274727587086192517348172902892, 2232503899320641354611543193546932867000021, 6176723085884734212324298659769446263070448, 17089290336110005967265144047559885713675750, 47281355346396015560792186405540324527603861, 130814474191283492096176478080389100516559077 The two last ratios (giving appx. to the "connective consts.") are: 2.766724288, 2.766724329 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, 739, 2510, 8380, 27536, 89238, 285972, 908394, 2865583, 8989689, 28074486, 87345748, 270883172, 837770117, 2584785651, 7958080095, 24455887983, 75031160980, 229859421044, 703257548672, 2149108480642, 6560654178624, 20009099465614, 60973454527345, 185662196634304, 564947472504283, 1718001255645543, 5221502813756162, 15861610321791453, 48161438474526547, 146174164181198265, 443483532748062491, 1345039828449306184, 4078093147894004461, 12361061251033686747, 37457784955117587075, 113481792557806090771, 343729769435341497863, 1040934076602837914284, 3151751141885038656629, 9541354498479408118898, 28880436459826255622687, 87405489100322852973284, 264496553932236705273388, 800299134168502474000712, 2421251715648342402277647, 7324646535787953639825097, 22156240304670818919440734, 67014895447548728769259730, 202682120931587606792747456, 612958445814853114496755224, 1853619414224728692075369736, 5605137632078849266706897210, 16948458610043552808384732937, 51245320104943069142990788339, 154938730139051323828113034366, 468434752970010378448877875387, 1416194742669803184204608649710, 4281371378573823351819395175843, 12942854409081905959877822339042, 39126009581196893699242305690491, 118274294758226790236661607466199, 357524167682825268363038706361617, 1080715794360851284582351765206997, 3266701180474911163106505139991656, 9874152525316830172175615214216840, 29845812064806642341597602683168527, 90211249104762812535235082056778326, 272666794316594170167322494161206328, 824135371915143469134631971945381909, 2490921539749143832595388169050768783, 7528650571934849083123756183775539689, 22754652358823461969276192137297817408, 68773255326896527220472337603102269912, 207857444620052739539587396248723286670, 628215281533706406758198160368421291463, 1898666035336558822933012130378710971661, 5738337372440881308087192061063124227703, 17342879441386463189289248216850717763901, 52414827795432737588040212705940564039324, 158410927232405207378204562451722740168406, 478756067831162085710522092250764829383239, 1446910881860405442891978043244815238680358, 4372881930714848961697985226181931833429439, 13215765554351742240975391881469078997268974, 39940695558618667492730294426607336178646445, 120708472275017594969941414505004211183769449, 364803346333933586692566566097527167963550733, 1102500752001544062241226783607661221932104245, 3331946956198902262374573348493434219148243999, 10069697932092610248557366288252306554513232585, 30432249488447835533367556439878427072609054507, 91971015285351536163473147196363066960557775872, 277950382668082415351888367011215447974027345096, 840007174654340149276139225163631552311332767430 The two last ratios (giving appx. to the "connective consts.") are: 3.022147934, 3.022151944 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, 2700, 9606, 33927, 118626, 410443, 1406320, 4777954, 16118309, 54056091, 180407942, 599655266, 1986351387, 6560430753, 21612163053, 71037483273, 233028604700, 763051151506, 2494579563244, 8143408995890, 26548366273208, 86445560985034, 281168042116585, 913582573981481, 2965680418733593, 9618959491259263, 31173703961466550, 100955937555853177, 326725173427507375, 1056726348137728488, 3415794010610905941, 11035404508793196778, 35634361618717159743, 115013586656395728681, 371058846301346386513, 1196638083057107633597, 3857634908392508916549, 12431646654738258201773, 40049356507426371644471, 128982601320571868093706, 415282932434481042821213, 1336726067811329053273543, 4301635193084308179897398, 13839629633988619874616072, 44516551177449313375029393, 143162962155605283596461681, 460317535543087992980093364, 1479814295792259796600344701, 4756468207530425664393487014, 15286010705586371058400570143, 49117935313532699695094029768, 157807031930280601512812599919, 506940012851659950560824082393, 1628299125402312290349602830649, 5229527021437774703503065923678, 16793616693512160863966252919899, 53924046280103231837110698383560, 173132958522182097994324056722074, 555825584355537626619036577765344, 1784272289143159609126572486602552, 5727297038327617317810270590768089, 18382572822985394436389772680814483, 58997389781424805879096400389675607, 189335043073078927130169045090285347, 607578767504741190510117100850859092, 1949616224049269230175447097112410595, 6255645174371293588337659838917545368, 20071180149545150252801558513723494458, 64395102839468075935911377266395691925, 206591824133319363128779693670844274421, 662757925080687434387862966091808376647, 2126078632526777845376651825145123403948, 6820046390205053465140023102860229332198, 21876604012409606473105478828559693498677, 70171046713976437311027036732922015976329, 225072442243829650881925037621279676506404, 721894626424896168663468238385252675101683, 2315331400442883212937314917869402588160166, 7425763050377865865928313156934174544238782, 23815420253821545607519938847894722596962917, 76377471022501986221919651613835083480393969, 244941711999618397964679562206799725900897971, 785509113333584401924474961198999207347298743, 2519017777758516316580484229147939382499297497, 8077988922188174851524396183843137610529776213, 25904054931737329577206147729878166180805766103, 83066357130656183748003389456940583567272327789, 266364228504505940953111970867667351412894844610, 854122859549793151933990837110785988339959956569, 2738790813439747217187898387884920271281067729798, 8781966865001737205629917835497970685936515966407, 28159144910201581736024166029899699006890490738152, 90290523669692858026719945536643576627099275511492, 289507758935395016660425172528317257414024274875257 The two last ratios (giving appx. to the "connective consts.") are: 3.206402479, 3.206436984 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, 9881, 36037, 131384, 476990, 1720943, 6165759, 21938442, 77563438, 272678463, 953912745, 3322985388, 11533739050, 39907348120, 137707580767, 474060125826, 1628549262819, 5584185615486, 19115810527459, 65338412980178, 223021152554386, 760283496469735, 2588815123240998, 8805645474444040, 29921991956324668, 101582728430028227, 344569819544696576, 1167852348868045770, 3955260502365912041, 13386277806267681991, 45275321994831073784, 153037567494143703499, 516994313836472543756, 1745580296741067963096, 5890799585223161237422, 19870187998103316775068, 66993864912989778118762, 225779535905806313207890, 760608156751951532304107, 2561379322573524108750426, 8622482918306135353387903, 29016479116039648709536239, 97615518820203688141576989, 328293399718852248514903117, 1103777280922619791250402644, 3710079527512875788382874155, 12467331696305950548746260810, 41884952488363694682591592593, 140683158325853147054289003554, 472422744461565942541306211173, 1586093689280366466734443568319, 5324032508364524323547813015431, 17867780207886746466727162217609, 59954602654815089333892021844263, 201140832773341528686221005653384, 674694706891123976191224818572590, 2262804695094777285274241262326726, 7587919814807407114533994172277324, 25441183111891627666840400530176919, 85289121592219676561696492984554858, 285887031432509868219071293551044271, 958169436719834960150252220164148475, 3210995196259018993343410487756861048, 10759418393513485519199325669161165239, 36048892970057834884988238698050801423, 120767799818439954651123236658775222882, 404546498824353099809005279211850959908, 1355019977866861949731973890118798348159, 4538211212594909012575272689500769575406, 15198025692351450041659049895830287292234, 50892611243303016781433660922200670458180, 170407589894609783057615783540562300166759, 570546766448627963467530788112081704095361, 1910130691268644566421526645096236032700132, 6394488001099828550696940838915612209858596, 21405264931311728034440902326450731380351481, 71648778744282908457918315532272548732739786, 239812321001175690978755418183494210930815713, 802619700900017892721011011810011484850727957, 2686116341029778314168362291512595931144284278, 8989126890624852755613268776896917104670759758, 30080763471514223767477972737541840558889994896, 100656023587576193337440644968135445803553016542, 336799263731883300660086720530263351839601027228, 1126895863474616808143481946004700473625272883039, 3770322714180157878611861423640989420291498441346, 12614095596569448253363686720889406443589857212672, 42200470846356111527186433115161928730489938520229, 141176613230619232468460198427464794421933992809667, 472273061140545340282912568743708832942231705982578, 1579825716790997333568784494316901810455492793538685, 5284591061143653750904008334336406324509042541183883, 17676666888835208606483658991996260462255561172793128 The two last ratios (giving appx. to the "connective consts.") are: 3.344945084, 3.345046865 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (site) lattice animals of width <= 8 equals 1, 2, 6, 19, 63, 216, 760, 2725, 9909, 36413, 134738, 500172, 1856709, 6876005, 25365540, 93139117, 340329647, 1237650963, 4480884742, 16157439370, 58051123610, 207901373113, 742465771624, 2644919804992, 9401360635950, 33351697121595, 118109506652766, 417607408711582, 1474459927009329, 5199175972983392, 18311343330350304, 64421516498615111, 226413522664164955, 794997533611816780, 2789003047024494902, 9776352271554908717, 34242995617527087081, 119854418512533187986, 419220295466966637689, 1465391012804326348357, 5119215290166512450350, 17873367737618126261148, 62370026233041825042984, 217532652950240697548006, 758339306699182353715308, 2642433448136539607378161, 9203563403837646666405234, 32042680525810550502998100, 111514507004712464438597591, 387946516916280303348906601, 1349143217939431406429081065, 4690263470139783773381201046, 16300324633269263334110204231, 56631952729013350126962293944, 196697642260289880762173854369, 682990755987465685620272086479, 2370903892647755353111600781255, 8228139120238727164864469785369, 28548459412634844546088155180693, 99028834062176817997638576348469, 343433704753246820960721720332873, 1190777228259603157554026147681850, 4127892421827379506053268294305072, 14306722494049412213935234661077489, 49575759271935084547357170173880720, 171758945786581869669586777695119483, 594967574921742822615234623726723802, 2060602335330266605423819423391170381, 7135508201655627887031734314669318705, 24705190268325461125644058482204713250, 85523739069032609255066120398687332861, 296021212090767376084233109479547999786, 1024469516909754416002823631014921324736, 3545010910821679857548012010487104380672, 12265368800334786208157578649948642062975, 42431679497527065515816264751749071691092, 146773751300747250583854042067680872808220, 507641394332424896974243858156350321109704, 1755569161798592750286438977171775554747415, 6070617674226944719196440290957969114821898, 20989568631442785276776221624655960468911550, 72565708051674012435951326988190358890575894, 250852358142026211565364841970584133176776621, 867092115236878284176163863681676139962678326, 2996912038762483832688050200988391578183234369, 10357282474413660627963478491155413902361252349, 35791674076586380887532916991923377393661297996, 123675541135894369937707369141012336149976582883, 427319235982836915954798573575643961546375318822, 1476349011740651084583073029770192206230692976686, 5100288133924588362901597066446864271641881165968, 17618564944789783064813799918280528465198393877791, 60857978622858695090995006103736922562393627105998, 210201917482449957801454646608211026937118360018084, 725987146075332404223098137604638915857856236242979, 2507235978587673714590872552250311905824272196184268, 8658375027068924260656259103723116009809095684384486, 29898770071387201070998766073542151000333470522440767, 103239720215010578398887049947440638680642573976922631, 356465632915563454604932676480739968910658903791124832 The two last ratios (giving appx. to the "connective consts.") are: 3.452795418, 3.452975489