The Series Expansion for 2D (square-lattice) Self-Avoiding Walks of Locally Bounded Width The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (square-lattice) Self-Avoiding walks of width <= 1 equals [0, 2, 5, 13, 27, 59, 119, 245, 491, 991, 1983, 3977, 7955, 15923, 31847, 63709, 127419, 254855, 509711, 1019441, 2038883, 4077787, 8155575, 16311173, 32622347, 65244719, 130489439, 260978905, 521957811, 1043915651, 2087831303, 4175662637, 8351325275, 16702650583, 33405301167, 66810602369, 133621204739, 267242409515, 534484819031, 1068969638101, 2137939276203, 4275878552447, 8551757104895, 17103514209833, 34207028419667, 68414056839379, 136828113678759, 273656227357565, 547312454715131, 1094624909430311, 2189249818860623, 4378499637721297, 8756999275442595, 17513998550885243, 35027997101770487, 70055994203541029, 140111988407082059, 280223976814164175, 560447953628328351, 1120895907256656761, 2241791814513313523, 4483583629026627107, 8967167258053254215, 17934334516106508493, 35868669032213016987, 71737338064426034039, 143474676128852068079, 286949352257704136225, 573898704515408272451, 1147797409030816544971, 2295594818061633089943, 4591189636123266179957, 9182379272246532359915, 18364758544493064719903, 36729517088986129439807, 73459034177972258879689, 146918068355944517759379, 293836136711889035518835, 587672273423778071037671, 1175344546847556142075421, 2350689093695112284150843, 4701378187390224568301767, 9402756374780449136603535, 18805512749560898273207153, 37611025499121796546414307, 75222050998243593092828699, 150444101996487186185657399, 300888203992974372371314885, 601776407985948744742629771, 1203552815971897489485259631, 2407105631943794978970519263, 4814211263887589957941038617, 9628422527775179915882077235, 19256845055550359831764154563, 38513690111100719663528309127, 77027380222201439327056618349, 154054760444402878654113236699, 308109520888805757308226473495, 616219041777611514616452946991, 1232438083555223029232905894081, 2464876167110446058465811788163] The two last ratios (giving appx. to the "connective consts.") are: 2.000000000, 2.000000000 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (square-lattice) Self-Avoiding walks of width <= 2 equals [0, 2, 6, 17, 45, 115, 277, 681, 1585, 3757, 8701, 20247, 46619, 107715, 247139, 568557, 1303157, 2990537, 6851041, 15704071, 35965607, 82394763, 188676631, 432120457, 989460873, 2265816417, 5188073133, 11879640335, 27200622211, 62281930407, 142605071339, 326521304185, 747623921477, 1711814055961, 3919473001505, 8974279416827, 20548040400391, 47048049210815, 107723962904935, 246651183519537, 564746890238881, 1293077566548293, 2960705399584357, 6779003429785195, 15521599033409139, 35539153978397415, 81372505089347227, 186315203730880749, 426598077872882453, 976763667403502813, 2236454640351906065, 5120716040250376275, 11724687883608452687, 26845524171134527651, 61467066193770273999, 140738553127913173213, 322243138327905488561, 737826543854963507189, 1689370365988300385029, 3868080184671241843295, 8856580305134758085939, 20278538955531275423163, 46430916669712527665451, 106310914588134682512245, 243415624128257124878605, 557338503768403039870401, 1276114501229002118658217, 2921865633272012075665615, 6690072693779422644847743, 15317977712102291579703875, 35072928490827326974998751, 80305007360918177583223633, 183870993518832040043071201, 421001670614150726128307545, 963949795820192820054438709, 2207115253263990281225188759, 5053538848507716182033632347, 11570875084848197003048076191, 26493345404610800008579307891, 60660697274934838479179031873, 138892243983674094718691299933, 318015721965533593469214353105, 728147206183399874670408539561, 1667207993981382827415966101699, 3817335933711288794469025896607, 8740393330291490601965019292343, 20012510529543866135284256700079, 45821802584912811392856779886009, 104916251713201236800829017251513, 240222323273945053281646982303549, 550026937264959766105970405868717, 1259373515308454609402831880908595, 2883534502777183984425172662151371, 6602307518488628687972975785512095, 15117025486155514258083200078167267, 34612816641625958224286101496357301, 79251508636008788213883352909144301, 181458841853684271524183879892887253, 415478668527446971329401257006311705, 951304010528904941278270688766225627, 2178160731225591041857036064363582631] The two last ratios (giving appx. to the "connective consts.") are: 2.289657888, 2.289657888 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (square-lattice) Self-Avoiding walks of width <= 3 equals [0, 2, 6, 18, 49, 137, 357, 937, 2373, 6011, 14901, 37097, 90951, 223663, 544875, 1330003, 3226513, 7837583, 18964209, 45924151, 110934523, 268116443, 646989669, 1561764385, 3766221993, 9084201201, 21897800313, 52792262715, 127225573181, 306628944785, 738838558455, 1780357488987, 4289453622825, 10334982337477, 24898832233375, 59986862235211, 144513961844873, 348151510720725, 838711242577771, 2020503292208801, 4867410676392815, 11725683864425187, 28247051893709307, 68047024141552369, 163923788459969563, 394889391766364747, 951277109830433557, 2291601036297368393, 5520390866399510827, 13298445486723533939, 32035480292176094005, 77172352498607029823, 185905324314744986051, 447839090466545417449, 1078827291297249914475, 2598854098921643104163, 6260539013661089834897, 15081397372699731872303, 36330498127626896742551, 87518756680800888253249, 210829254961626931805717, 507879424842288809805413, 1223461572414992559474997, 2947270881869950909306393, 7099859512573940975675929, 17103282168982596127488827, 41201132653456010394906997, 99251905195357435573103085, 239093925425451885878354015, 575967838915386811736263963, 1387483801379698770803305775, 3342393745575435177079138007, 8051694643915236913359948161, 19396214701339002465353817875, 46724715754368983374764084937, 112557996355010028709800773869, 271147770848353602134982732791, 653184278712100754478683634235, 1573495146803980809655559515185, 3790487704973293565436146575599, 9131135270162646214331530301809, 21996544461290351449779729852353, 52988807387073991247716433667505, 127647945496721773334358118502855, 307498862295689202467716069489829, 740752621981434376281495609940999, 1784443827870992129109879906091361, 4298654747101092758329988476406405, 10355289611668135115554791658602381, 24945483936676951765894798107150855, 60092686167440738060242753368406597, 144760909029348634437582596021206051, 348723315913302070281041833579013765, 840060703387433746991357556567585637, 2023673075935744813058549319998474757, 4874948562367148549534741087028370625, 11743558664740752295572360692054622951, 28289769286404124889877733652787768189, 68148937568349561985541278376791234665, 164168100654383462218820532358232547731, 395474474497157816593543559042215355349] The two last ratios (giving appx. to the "connective consts.") are: 2.408960528, 2.408960528 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (square-lattice) Self-Avoiding walks of width <= 4 equals [0, 2, 6, 18, 50, 141, 385, 1045, 2763, 7293, 18803, 48637, 123685, 315681, 795771, 2012317, 5042775, 12668201, 31615489, 79049567, 196708631, 490176265, 1217234335, 3025812827, 7502751703, 18617634865, 46115238355, 114287876321, 282874712171, 700418700225, 1732688152277, 4287503168871, 10602381499943, 26223387835665, 64829425186241, 160293820777121, 396203878728375, 979408581082371, 2420519719401839, 5982514718892133, 14783878443598875, 36535439999769379, 90279863462461863, 223091172832304913, 551238266512664229, 1362092997651820143, 3365503874056081361, 8315736021876384935, 20546343711659703705, 50766059417227396975, 125429800004777689205, 309907088502822065581, 765692209793569131861, 1891818091771341300671, 4674110125997357271231, 11548356582827152602833, 28532352048066468611279, 70494644026541947215671, 174169461262874865841527, 430317189304044258330813, 1063172039400649587272305, 2626751258532057982832875, 6489826535269718429716043, 16034211485288871114230323, 39615145727424306628273601, 97875764783637413469762237, 241817920896991843316475089, 597450564632213181761144343, 1476097550839318300153184151, 3646937041541237899836968135, 9010340261099098845471633867, 22261488586194776120449463597, 55000548301861439924952835983, 135887620561372201216048130597, 335731922658264937249157276529, 829479047747925887340151673465, 2049359330151082774601326339283, 5063267041638456119786285461285, 12509601966201114741063678248023, 30906951319468192663572016422569, 76360506921408508786947859355237, 188660703717429168100719734246969, 466116062008270101666623193604023, 1151613363363359714456509612619463, 2845242606094248833811613017254139, 7029621098375136111819376264669479, 17367788309361682242275290865310593, 42909862323748429081870128078713399, 106015585484179891932568126852968713, 261928233439704170178799660923729995, 647135024382057146815444391073928381, 1598849181162358413991791694502820243, 3950209126460481475408650017621311485, 9759614835249621590041501931378234953, 24112667976868823786822296694030306967, 59574149996525424924703985986868627025, 147187334696201104738026924883790584559, 363649527943287822129089599069356363695, 898453518737247078161007565113771578613, 2219771136863466907034910072342529778571, 5484294721004222397378336619088459487163] The two last ratios (giving appx. to the "connective consts.") are: 2.470657736, 2.470657734 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (square-lattice) Self-Avoiding walks of width <= 5 equals [0, 2, 6, 18, 50, 142, 389, 1081, 2907, 7883, 20849, 55249, 144125, 376219, 971415, 2511225, 6436827, 16523279, 42128205, 107563935, 273169825, 694604997, 1758818097, 4458085591, 11263086669, 28478652827, 71826103953, 181267234505, 456569968193, 1150551689295, 2895012787807, 7287127055817, 18321389559321, 46076989851471, 115777055320221, 290974842923667, 730787491333281, 1835688448248769, 4608706393904397, 11572152805194325, 29045243894744253, 72908436392939055, 182956354262197429, 459144112731125839, 1151991151574897145, 2890502677293101795, 7251376598216720755, 18192223688716557227, 45634417762602593413, 114475624526015870609, 287136952522365760545, 720237199939483084727, 1806460023516744270143, 4530947135811232502123, 11363815753809296168107, 28501339254111044777681, 71480425595137086036221, 179272396258262292973677, 449598877525902547626745, 1127561766712911509102447, 2827772980959058716025509, 7091714394597536574412471, 17784829740949773880811197, 44601561019764450311000657, 111852121326211593483037401, 280504474511977975323654375, 703445926974420338674622069, 1764097947633267119699273233, 4423959949654119338522060487, 11094314250549831444555699755, 27821921976810821855416695043, 69770908793529457422279691617, 174968422025858561088832993423, 438778569852587833583359909837, 1100347034087361432076750198205, 2759397540903851880154680228735, 6919867415846517689271126453615, 17353277743794377338413452628983, 43517550666344793347868963196561, 109130853341725410573471255892401, 273671799145569277676915040750469, 686297913962504899943400872691837, 1721055414736945490937675771681527, 4315957207463792044082233610334207, 10823284279956640706714969045676461, 27141951880922781594544486703653541, 68064840794322144956604465345477499, 170688650844288601989823054638227981, 428041886241461248540967907849940931, 1073415678090009302677077817514134009, 2691841339239050491591290547669393789, 6750423399115295542832206341004517941, 16928265571737758599657641497543982815, 42451587618640934793266829546952514651, 106457271718466900617105248952175318717, 266966485392947196724602917215911280495, 669480756495653491522253066370938144653, 1678879263432367410962890292525970970423, 4210181209872268848659091358809101114227, 10558011280928550472974048025331108693975, 26476673670172505026463931885219868227153] The two last ratios (giving appx. to the "connective consts.") are: 2.507733220, 2.507733166