The Series Expansion for 2D (square-lattice) Self-Avoiding Polygons of Globally Bounded Width The first 100 coeffs. of the generating function (in the variable s), enumerating 2D Self-Avoiding Polygons of GLOBAL width <= 1 equals [0, 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 quare roots of the two last ratios (giving appx. to the "connective consts.") for the counted class are: 1., 1. The first 100 coeffs. of the generating function (in the variable s), enumerating 2D Self-Avoiding Polygons of GLOBAL width <= 2 equals [0, 1, 2, 6, 14, 28, 56, 114, 230, 460, 920, 1842, 3686, 7372, 14744, 29490, 58982, 117964, 235928, 471858, 943718, 1887436, 3774872, 7549746, 15099494, 30198988, 60397976, 120795954, 241591910, 483183820, 966367640, 1932735282, 3865470566, 7730941132, 15461882264, 30923764530, 61847529062, 123695058124, 247390116248, 494780232498, 989560464998, 1979120929996, 3958241859992, 7916483719986, 15832967439974, 31665934879948, 63331869759896, 126663739519794, 253327479039590, 506654958079180, 1013309916158360, 2026619832316722, 4053239664633446, 8106479329266892, 16212958658533784, 32425917317067570, 64851834634135142, 129703669268270284, 259407338536540568, 518814677073081138, 1037629354146162278, 2075258708292324556, 4150517416584649112, 8301034833169298226, 16602069666338596454, 33204139332677192908, 66408278665354385816, 132816557330708771634, 265633114661417543270, 531266229322835086540, 1062532458645670173080, 2125064917291340346162, 4250129834582680692326, 8500259669165361384652, 17000519338330722769304, 34001038676661445538610, 68002077353322891077222, 136004154706645782154444, 272008309413291564308888, 544016618826583128617778, 1088033237653166257235558, 2176066475306332514471116, 4352132950612665028942232, 8704265901225330057884466, 17408531802450660115768934, 34817063604901320231537868, 69634127209802640463075736, 139268254419605280926151474, 278536508839210561852302950, 557073017678421123704605900, 1114146035356842247409211800, 2228292070713684494818423602, 4456584141427368989636847206, 8913168282854737979273694412, 17826336565709475958547388824, 35652673131418951917094777650, 71305346262837903834189555302, 142610692525675807668379110604, 285221385051351615336758221208, 570442770102703230673516442418] The quare roots of the two last ratios (giving appx. to the "connective consts.") for the counted class are: 1.414213562, 1.414213562 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D Self-Avoiding Polygons of GLOBAL width <= 3 equals [0, 1, 2, 7, 27, 98, 310, 917, 2673, 7742, 22282, 63805, 182011, 517832, 1470660, 4171661, 11823191, 33488608, 94814066, 268359307, 759394945, 2148588416, 6078444650, 17194873063, 48638742759, 137578112446, 389139025528, 1100657127515, 3113103300351, 8805031727594, 24903788979882, 70436519205997, 199218148262085, 563454549417598, 1593632425915286, 4507304666946189, 12748095560922183, 36055660046798032, 101976806986199752, 288422569151061621, 815749811600518139, 2307196899236834480, 6525477422492752046, 18456098165113972907, 52199635322399265053, 147636938380462835544, 417563549490090637918, 1181000612501608639775, 3340239899503543144731, 9447245298178129244446, 26719770384352046242788, 75571884033343673496907, 213740969911823558325163, 604526441257035421443218, 1709790208846054706268622, 4835822480857465523127285, 13677221290868148240485641, 38683467573983853431899630, 109408967736597068992041714, 309442843893234741894288461, 875201325797998710191260099, 2475343591505725724247518536, 7001047318796694630928365980, 19801155574806801333031644237, 56003872595615518262782899215, 158396500332721719598292482864, 447994935960557350127873553210, 1267070056605503591497762502459, 3583671152182871113911630274537, 10135744949476585361164723599648, 28667062717964642132684260002722, 81079436091617714379840906961735, 229318051227976210536750077198271, 648583304889501040891244142373806, 1834396817555892850927445997996832, 5188249001920734274296328649038507, 14673993897228251926304333584929927, 41502652786336080070353191705734826, 117382506791681308499067004002027714, 331994510607080571860856298960602733, 938984505321743138722070555393796541, 2655742408577615127617706314062655246, 7511271699100328984957540606736769182, 21244229995905005510133626762774942845, 60085339233960156151477174476539188591, 169940166885589584579937902604936508592, 480644042112332361129099572450327876800, 1359411959231559138399483693386219578901, 3844842987713271083566497162634292799123, 10874420737422475054810185795971756926944, 30756269307323387419245324906883908890262, 86988366971058834612037666678092095638587, 246030359296203731048392661455694755154661, 695850948846501579533211342256193108797784, 1968084525810986708656738673830454978077110, 5566359731430185316000840640853279034737759, 15743409519934010385163960470958248206007507, 44527295264955218287515288530946303893820142, 125937143482297802575139245406052274237333932, 356189703733553516653173487856901158929851003] The quare roots of the two last ratios (giving appx. to the "connective consts.") for the counted class are: 1.681759004, 1.681759004 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D Self-Avoiding Polygons of GLOBAL width <= 4 equals [0, 1, 2, 7, 28, 123, 546, 2269, 8748, 32331, 117230, 420759, 1500244, 5323039, 18811158, 66252781, 232686226, 815345341, 2851760560, 9959693801, 34743096496, 121082553339, 421662141270, 1467508793555, 5104819351912, 17750243772405, 61700048287440, 214412775030465, 744940321160102, 2587709936710987, 8987673762284148, 31212476209812639, 108384658712687524, 376334256549784077, 1306628987744028882, 4536370414035302755, 15748766877023883836, 54672608459187397819, 189793343066166392438, 658843601104267443297, 2287050137619006677334, 7938939973827071757909, 27557767940386462745590, 95657985555957835566049, 332043433966573749214156, 1152565695091708369752077, 4000682997205664177877894, 13886752150123349955819791, 48202068314575604426614854, 167312888531985020662294941, 580753837629111065215304352, 2015830160522532155177751527, 6997052042417881770784555390, 24287102808420559769836444957, 84301608940988266557553175804, 292614366603931679520524296887, 1015675846244412275366973905540, 3525448364284865507979250871929, 12236955793260629537280706758734, 42474889794961543536303006503881, 147431742054217363563623881446664, 511740306817928661468938939290513, 1776266661927124399381248944560444, 6165476295242305740490168921439559, 21400555234737216827291923428221546, 74281968171333453457349700760392099, 257834913150483209878010482110635050, 894952560029664587225429287321746065, 3106406449003559366773188007808855292, 10782426900559119802406384410462703311, 37426115086972720896118519165322159436, 129907121863791472278472468670296895449, 450911344351979526032757958684650306732, 1565126170123119215860774543222084755423, 5432597596787183240711170651147128426592, 18856701007670194943801114803541235266995, 65452145578823052753934528781958307245186, 227186256955321467062644760109135448813359, 788569946732594622255246648393138113952726, 2737148652073848094003286596869098596394683, 9500720559229636467078307514804179054820634, 32977270233680289888900440903700064003284271, 114465038898926898414973113602463621475622124, 397311390576345423509903854816694042426264925, 1379079081656870412348075880071285076034463604, 4786822515251929275782526892767740718812148639, 16615196374934901322197478828505683999585823448, 57671816609454768164057859297092001533327770497, 200180506608591898535640777942990035003858548030, 694832199669560282786666522073127957186082612475, 2411782213758188976038868300921018627992479199270, 8371364260673833265835376757895780081775711822277, 29057242048834564805376006039971353637340103567936, 100858508708087968254805146948419905037982150328615, 350082735270271242087773595164933725061883810820424, 1215147071627240798475328656554661021807328794021619, 4217809839321825696800219515736920572161399866595452, 14640137192663361432862765313298887776488292208532111, 50816330075951831974395542326347274422524805587800478, 176384918265170121089540189818643505043346194129822181] The quare roots of the two last ratios (giving appx. to the "connective consts.") for the counted class are: 1.863069583, 1.863069583 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D Self-Avoiding Polygons of GLOBAL width <= 5 equals [0, 1, 2, 7, 28, 124, 587, 2876, 13871, 63743, 279648, 1190000, 4973143, 20555849, 84364308, 344527790, 1401594061, 5683628400, 22983351905, 92710607969, 373168738900, 1499213731676, 6013350767807, 24085956772925, 96358960136530, 385101273652155, 1537711892136828, 6135430356469961, 24464140265718442, 97491767799178335, 388321730511248314, 1546070644515996461, 6153258309904007624, 24481619610168703174, 97376138019908538461, 387220335524987167874, 1539468150270234737339, 6119305480368877932197, 24319957538512425761310, 96641079783437249781815, 383978475845676917761550, 1525474600269086821632729, 6059852363276197936090230, 24070398037745006411474232, 95603370751316114535172567, 379695807228873149048342963, 1507906863188308797153983212, 5988145861202797089064608163, 23778912730914896338470638496, 94422541412256106385395231790, 374925911913890933256708015841, 1488685851320527853671122360671, 5910851265324150818733157883178, 23468628344664644554748543628574, 93178831370296983843473034926083, 369947170220752766256443001409840, 1468777301343708283513839896842903, 5831318572715338207842919510587436, 23151164456859057021863984485878159, 91912539292466670869674937927896408, 364899327985536021573321160504447097, 1448665750834718990391403603428885322, 5751227545732075734309348297397113419, 22832343307520842807289388597172614231, 90643841538337953874953972402682812700, 359852287717576717200339879582515381447, 1428593316506385813778404451229562230588, 5671416526476308138625671312707209678120, 22515066660359198166749954891317933967435, 89382777875875063022328570369769438739626, 354840769366938099244967977230927696185595, 1408680002684217289597462406674879731976256, 5592300030309631967521504455196556410739691, 22200765278737473683878170209020924532579203, 88134282642651590406425968813199472988006132, 349881773590312389471725451663514458524741786, 1388984316671297885567171940351650708571215987, 5514079143061242651681316513178709911311222716, 21890129218716687231102053507185172519366139943, 86900719607435192219926041677555826553440615487, 344983380302675917645357011994142573972924837366, 1369533808671656582367802744592548763926374343188, 5436847525572289156878510681743753984337322802591, 21583475772254916274412642648563319584956457216183, 85683159105172561568341768355863410209441959717464, 340149181624017742240135796705276842212923227712679, 1350340458574732611067183038694127914476134176836480, 5360644821266941833483779725740841429195176083248583, 21280934844837397353599979523600190944860302191311788, 84482021481797293126691794766885122852545103409783081, 335380515269902354338282742985147664693181794632342778, 1331408428019686801345894354588113925170060306079910167, 5285483563399850524577644035309968464782355993076763156, 20982542349757146851501704155455306742188888016261354670, 83297401262320593432331331671594734978117692041449813735, 330677589723870175368756136188845102681983631982806004296, 1312737965804515433427877789253653659286845973892506152261, 5211362730460093925018161779965179117646490539179723722501, 20688287257790821491378167234224569079117328289038684435728, 82129230455574130074459908388595559533359581482787993159751] The quare roots of the two last ratios (giving appx. to the "connective consts.") for the counted class are: 1.992446221, 1.992446265