The Series Expansion for 2D (square-lattice) Self-Avoiding Walks of Globally Bounded Width The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (site) self-avoiding walks of global width <= 1 equals [0, 2, 5, 11, 19, 35, 57, 99, 159, 267, 429, 707, 1139, 1859, 3001, 4875, 7879, 12771, 20653, 33443, 54099, 87563, 141665, 229251, 370919, 600195, 971117, 1571339, 2542459, 4113827, 6656289, 10770147, 17426439, 28196619, 45623061, 73819715, 119442779, 193262531, 312705313, 505967883, 818673199, 1324641123, 2143314325, 3467955491, 5611269819, 9079225355, 14690495177, 23769720579, 38460215759, 62229936387, 100690152149, 162920088587, 263610240739, 426530329379, 690140570121, 1116670899555, 1806811469679, 2923482369291, 4730293838973, 7653776208323, 12384070047299, 20037846255683, 32421916302985, 52459762558731, 84881678861719, 137341441420515, 222223120282237, 359564561702819, 581787681985059, 941352243687947, 1523139925673009, 2464492169361027, 3987632095034039, 6452124264395139, 10439756359429181, 16891880623824395, 27331636983253579, 44223517607078051, 71555154590331633, 115778672197409763, 187333826787741399, 303112498985151243, 490446325772892645, 793558824758043971, 1284005150530936619, 2077563975288980675, 3361569125819917297, 5439133101108898059, 8800702226928815359, 14239835328037713507, 23040537554966528869, 37280372883004242467, 60320910437970771339, 97601283320975013899, 157922193758945785241, 255523477079920799235, 413445670838866584479, 668969147918787383811, 1082414818757653968293, 1751383966676441352203] The two last ratios (giving appx. to The "connective consts.") for the counted class are: 1.618033989, 1.618033989 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (site) self-avoiding walks of global width <= 2 equals [0, 2, 6, 17, 41, 95, 203, 441, 899, 1869, 3705, 7453, 14577, 28817, 55923, 109323, 211125, 409641, 788845, 1523355, 2928093, 5637515, 10822717, 20796965, 39892485, 76562051, 146777963, 281470321, 539401223, 1033844005, 1980695067, 3794988521, 7269280645, 13924666195, 26669102533, 51078172385, 97817935973, 187327164951, 358719743113, 686921718901, 1315350432543, 2518678565469, 4822725640723, 9234419540915, 17681502272511, 33855276444637, 64822925517709, 124116347335513, 237643560680707, 455010719585007, 871194225058091, 1668042884187489, 3193728024448493, 6114877952204387, 11707835875349049, 22416346168723695, 42919268564688341, 82174928200446289, 157335187034660585, 301239589716210335, 576763660748313167, 1104290876386358523, 2114310843375577237, 4048125896952301995, 7750665860981080915, 14839657877169791461, 28412447285881179363, 54399299082491996477, 104154462093455730793, 199417096894078435531, 381809595498533497795, 731023333982252939889, 1399637590953410390813, 2679784815207216269907, 5130789714452164532825, 9823550548522669047775, 18808438070679055342337, 36011147543120500463267, 68947920967947383814667, 132009557903240802990431, 252749070533607174779577, 483920197398183544263621, 926526664413554183963499, 1773952919594405092381113, 3396458020701532631717201, 6502949901080328069153829, 12450722715518802906054929, 23838488272508128852387973, 45641809910026226063854659, 87387034641981496833304631, 167313561910530274841166065, 320343034920468766738580621, 613337367936203350715903249, 1174312174295173657218690045, 2248369578521197206620927507, 4304788677322512899289194997, 8242063805772728178589178993, 15780476295992837437082399601, 30213722885027559182836710711, 57848003604111599465924529065] The two last ratios (giving appx. to The "connective consts.") for the counted class are: 1.914626801, 1.914626803 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (site) self-avoiding walks of global width <= 3 equals [0, 2, 6, 18, 49, 131, 323, 785, 1821, 4251, 9585, 21763, 47949, 106325, 230611, 503203, 1080473, 2331455, 4971659, 10640205, 22576941, 48027569, 101536739, 215037533, 453386103, 957024227, 2013648621, 4239967989, 8907116277, 18719903621, 39277559083, 82431298801, 172787905507, 362230722415, 758705256715, 1589190554751, 3326569683683, 6963227475609, 14568521979307, 30479039211431, 63742751159011, 133301451874023, 278689767722843, 582611820775845, 1217720542084487, 2545001717807673, 5318133510154753, 11112298089867095, 23216384455182633, 48502141047829003, 101317582912863759, 211634664161059835, 442033440815626241, 923217522722891707, 1928084252862623489, 4026530514161975267, 8408417089858346735, 17558312305946339093, 36663476110897254039, 76554692870769112497, 159843718260157324607, 333740146220761608981, 696802152235884642921, 1454793088086728072489, 3037268616253263921011, 6340992987636077760035, 13238026719302014625011, 27636467039439394940205, 57694587920847422978823, 120443104626677057378321, 251433543101732158254567, 524879580128790874419861, 1095699527676653799246765, 2287279328446319642155523, 4774666447196142157987729, 9966976556100699016209145, 20805615793483057299022435, 43430498567512686259289305, 90658039600704575147381543, 189241067583899356027041465, 395022801571077255972097489, 824568768197859534961960941, 1721193415353593179254355049, 3592780922839022793616125293, 7499463277335483024210270263, 15654102334267789018603323139, 32675692424001544369191273139, 68205626082984009111841222331, 142368681141399008327243102153, 297171863761876636348748695873, 620297395218349050163920000287, 1294766203684702582903327781835, 2702601092204442202857543468189, 5641204023732812276238778866313, 11775002008826184304276420312147, 24578170631508857556910639556301, 51302384511392810798676035950421, 107084109101130204447690902535619, 223517754676346221433798991679335, 466550422244582915998095337946285] The two last ratios (giving appx. to The "connective consts.") for the counted class are: 2.087308111, 2.087310214 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (site) self-avoiding walks of global width <= 4 equals [0, 2, 6, 18, 50, 141, 377, 995, 2499, 6235, 15105, 36659, 87067, 207365, 484421, 1135121, 2616297, 6050537, 13807805, 31613163, 71623331, 162724789, 366663509, 828042585, 1857918621, 4175862663, 9338321429, 20909698819, 46634996841, 104107093331, 231691609935, 515970841669, 1146289966733, 2547750778463, 5651989402951, 12542079756743, 27790484585475, 61587854895121, 136329244584069, 301799077872965, 667494378455787, 1476337075788803, 3262918879433759, 7211351828223975, 15928452179584541, 35180961010552887, 77667229972778825, 171449914217161001, 378330507141649531, 834776484414149311, 1841339898484703901, 4061255048343458655, 8955200686187690231, 19744783977674641933, 43524831172004755271, 95936620969287213259, 211424076767094378735, 465895430420872646677, 1026495977557875681169, 2261475475211889280023, 4981625659251592414969, 10972819777128255614693, 24166733950505594194863, 53221593477517184587687, 117197111956820510804227, 258058649177121155325863, 568178112898778401025119, 1250907767555565137544715, 2753817813726892418588653, 6062084404867957054760483, 13343867501530340049931147, 29371109828318724266814231, 64645042592858725971737271, 142275753922822148080833949, 313116238734431045671281027, 689069232742378094358049207, 1516357345166731381954843527, 3336756113206460191622736555, 7342279100523358483446322699, 16155597251234581795671264419, 35546797754683867073773056395, 78210492981077556867264009243, 172074490182847944786010177383, 378578793924623237226094900843, 832883775988458822224415623653, 1832322777605926720764905567539, 4030965863388567578916291424621, 8867613358367291237838915850115, 19507204310249164475268871334215, 42911602944659836937663444504695, 94394364732709886047810899854299, 207639351391473461761623792944685, 456736529404209676810653769611181, 1004650163338899657329467669344153, 2209821673175279740048363946327275, 4860638410398032848485424111736883, 10691123470414637356715549941781639, 23515147847007166658049891885700441, 51720967617704022783730034014812997, 113757612102345662019212563308437849] The two last ratios (giving appx. to The "connective consts.") for the counted class are: 2.199448644, 2.199474481 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (site) self-avoiding walks of global width <= 5 equals [0, 2, 6, 18, 50, 142, 389, 1071, 2839, 7465, 19021, 48245, 119913, 298039, 729653, 1788519, 4326113, 10481323, 25090559, 60177019, 142816915, 339638781, 800552375, 1890755609, 4432671001, 10410836435, 24302352641, 56817868767, 132169904743, 307846022829, 714059982879, 1657976284103, 3836573412815, 8884951012517, 20518824501163, 47414953582341, 109315285655213, 252141909268905, 580482827478667, 1336835202892725, 3073913778256939, 7069779801361303, 16239173799695715, 37306765912385255, 85615389207824119, 196496314816629515, 450584688247241477, 1033274359022907657, 2367765229931618877, 5425786466613900109, 12425760336989046139, 28455893717067756927, 65132913868329831183, 149076403917439158425, 341060404239948422951, 780238759446939439325, 1784293766131823066747, 4080136874155578469041, 9327155290908104117301, 21320161873266432974057, 48721113507513158106801, 111329231610943881597765, 254332920538826895441827, 580979279558950694487061, 1326884983592378192966949, 3030195859321888754161899, 6918846319301382294440581, 15796542727089525420151405, 36059953548589817522221801, 82310381372748499569659279, 187856637716128066677302311, 428712374180042392978705065, 978260467458762615568149499, 2232091048949524069307571745, 5092415969132465711504418033, 11617327432502633437137081113, 26500123738203743633081123909, 60445154652269826957083909241, 137860067230914831989594198381, 314404633709052273361219089521, 716978830685783650358748998439, 1634928305336916785346934028967, 3727873111997363626227380504625, 8499629727278247777071324714389, 19378119369377281029521275475113, 44177503186013365128430226632603, 100708430553032647516210382274727, 229567177754386583260837337551785, 523276220510973089303666852652177, 1192704430290393091669987581353159, 2718402673632034157639226470047103, 6195503832042836450792654755451079, 14119531405516951983376670355900981, 32177108188508650352650287773642727, 73325675111236898024742048832856141, 167089563034507135111489948368646705, 380738050564267286569099829628436527, 867537961866330702137676536151234177, 1976676705736862828229238974426535033, 4503695680213065549122709395879087219] The two last ratios (giving appx. to The "connective consts.") for the counted class are: 2.278417946, 2.278490156