The Series Expansion for 2D (square-lattice) Self-Avoiding Polygons of Locally Bounded Width The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (square-lattice) Self-Avoiding Polygons of 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 square roots of the 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 (square-lattice) Self-Avoiding Polygons of width <= 2 equals [0, 1, 2, 6, 16, 42, 112, 298, 792, 2106, 5600, 14890, 39592, 105274, 279920, 744298, 1979064, 5262266, 13992192, 37204778, 98926280, 263041722, 699419280, 1859732842, 4944968408, 13148508218, 34961450528, 92961346090, 247181159144, 657246565434, 1747596982192, 4646802848106, 12355695809272, 32853388431034, 87356078367552, 232276936784682, 617616728798984, 1642222551117754, 4366615704603856, 11610687417923434, 30872435642686232, 82088790112503610, 218271390703540320, 580376442804956714, 1543201856538460968, 4103322937288959290, 10910600616726292976, 29010927883818467178, 77139102258941145912, 205110333635153344954, 545381625296884770176, 1450151788746805177130, 3855905870060801814344, 10252726779462178346170, 27261663006478768860944, 72487864532541319696746, 192742845630485764946776, 512496881806470387312186, 1362712338308509178964640, 3623407249684460275135018, 9634520601290370503859048, 25617873128882219640782394, 68117081358423730335693872, 181121077048310421319888234, 481594981712809012257035128, 1280545203190775906505346234, 3404927542190981667907504064, 9053590250998357266834424618, 24073198450569248014587045768, 64009842236518816631823524282, 170200063425603595811902943568, 452556365988864504284803502954, 1203332479876370237645156998040, 3199621452592812171198923386170, 8507688117039723588612610776288, 22621662646424999823714458934826, 60150256315075347578439375418280, 159937551510655142157818431323962, 425268684629235631541505155935856, 1130775433399277100397707494032234, 3006694654449100116652557006648248, 7994702111555948596785831819200442, 21257649744359551511019635633113600, 56523390909173251852130217098724138, 150293835785817952408851733468962760, 399626361969528259691872955302876858, 1062593341543220975496858078272164752, 2825400716627606115503292578785131882, 7512647498737489725887189146448182232, 19975882397189027518271387028225825850, 53115213726370756993436548360470097696, 141231604847405520956918862042062385706, 375530188215559853943817046501046520808, 998522408731266742831426051765095622714, 2655038215372904381520506874115362537648, 7059659215908195213760073892997913739626, 18771401464651828294703506763641381262328, 49912538575957660566208101168511401339578, 132715797048383539854639856886660011420736, 352886935602028396864894828469114186705706] The square roots of the the two last ratios (giving appx. to the "connective consts.") are: 1.630633951, 1.630633952 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (square-lattice) Self-Avoiding Polygons of width <= 3 equals [0, 1, 2, 7, 27, 104, 384, 1403, 5135, 18820, 69008, 253033, 927735, 3401432, 12470952, 45723401, 167640095, 614635006, 2253495200, 8262204949, 30292511967, 111064333406, 407205787164, 1492977520847, 5473846265603, 20069286053086, 73581942774944, 269780513778403, 989122098032127, 3626512942368704, 13296231220928460, 48749244105796379, 178734015782291651, 655309615228808644, 2402624312623310612, 8808971291521609345, 32297173889048994579, 118414217358550120832, 434153369604650372004, 1591778019089886419753, 5836087980533280348083, 21397407495298304066734, 78451361433727301875460, 287633729093474608509997, 1054579048728276568678443, 3866504020657524402635174, 14176133462720431420389816, 51975313844025676763861471, 190562063787635655216011063, 698675918802114863943424558, 2561622338735671187981279252, 9391920960378958328932632187, 34434498010172000181239068587, 126250493186081472727015643000, 462884257090675334587739981064, 1697116819548454528368466245995, 6222301698694523287637938912295, 22813419785609128819454852384692, 83643022713542817676648848765800, 306668413346405230069605782210761, 1124367731980285622137997728402527, 4122376944281113391140384935214424, 15114264832920746064842734547605296, 55414874604462401786438387112361145, 203172854344836547106470411603668215, 744912066250603228144634527216525582, 2731142347904141741308892121651532856, 10013448381981163284300182518178012149, 36713263435553614896057912280315130151, 134605348794106715449511406957578945054, 493516463220124199497056143449048848612, 1809426606381362964278221965240422027231, 6634073810867897303235134424699507796379, 24323139260154860987090103811371942518062, 89178251604573147526535880097146856891736, 326962752389303196667011056298823742271043, 1198774808055405060133643660901938641613703, 4395182723190483057156523281306918347714144, 16114478749823116693787876427496125779642580, 59082054543115901206458236910593632178046251, 216618186863415513376764983926074862586002235, 794207974703225811395369008538876579380354132, 2911880651461262088063447895762412992212960908, 10676106509158204998468357618108769842087903169, 39142830300305151576695515102634360505240215643, 143513102141137752174930567083665670313180615008, 526175811206275338995460763052302229063111402316, 1929168697268514028177757007735984930710824671545, 7073095690181186062854669417852796896280280847467, 25932767161987781853430359810401163757939216980766, 95079784317274619222096044120070658323494105227068, 348600106164934219235974147595618698393317074977261, 1278105907483896298314205653889040291851712002402899, 4686041919827601596833666976490770058058199860551878, 17180883638673135494046109570185241007867030462281632, 62991916772371926647217078823454081281194000930924623, 230953288672868013561092021591867454611219027613700271, 846766129399758500957150567577046532223900137652741598, 3104579640406228909623129483969458576954681386195599980, 11382617241028746437864532225993374533295345117835176635] The square roots of the the two last ratios (giving appx. to the "connective consts.") are: 1.914783444, 1.914783443 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (square-lattice) Self-Avoiding Polygons of width <= 4 equals [0, 1, 2, 7, 28, 123, 558, 2499, 10950, 47483, 205232, 886659, 3832490, 16574285, 71699850, 310204437, 1342095364, 5806468323, 25120829734, 108680620999, 470185111166, 2034161659081, 8800396798920, 38073188125143, 164716212224306, 712612587207899, 3082979498149626, 13337909866082863, 57703866431628876, 249644525215059181, 1080038351896090678, 4672575295476588787, 20214985757022167950, 87456193529206809889, 378362165586758503064, 1636910121308701265785, 7081772410077799860722, 30637907246520747980619, 132548930702638085822410, 573447099011361853494937, 2480907040295092502391436, 10733160483670004871023507, 46434925653059917064871158, 200891650104973106414284617, 869118546316599808013636926, 3760071895257102290988342265, 16267217766116178622007556864, 70376945234487074080384633173, 304472128654638212430199087074, 1317239286510808943655196100425, 5698778885260929309996228265130, 24654655471991421721276198393053, 106663558751984301709856721826100, 461459085427611159491640241937497, 1996412739413927392600134712226462, 8637090376931046821191868645428211, 37366687111591205712920463668020766, 161659684542016140657010044414032323, 699389098321146302224944163863516512, 3025770539118767402740369468082009321, 13090406152134703121253989870427897210, 56633089327967681448841397350862335697, 245012016400005967537991196799779481762, 1059996706744216812167003844744631906671, 4585869031313999704981675771363007857300, 19839868028419739891092064779165880838321, 85833319856569654347127458196288131681158, 371341119156981109498234474484664365230541, 1606534933137680139982696818872106232196422, 6950360081994084691841105674473307593457849, 30069377436461173786302458675476868647355136, 130089297352915170829546817870070850488394007, 562805975000154662657043602600027407780866674, 2434870292492794775516217288380632620610611881, 10533991472393872092505256277771961177111459010, 45573259767715196631264806883224980475399409755, 197163820694043490620044216940319745101784061700, 852990819371046463391034960601649126529339910359, 3690298429854227874271854873398885984651732000414, 15965356475262004607429893163251767512180090976241, 69071001228553498371606553151895140014811782899318, 298822216597988369304048602177160467780589320872143, 1292796043842799052118412224960604937220377600066136, 5593029962775677769711297372124568528857370282457321, 24197153381999608676087061077906557215720507963750666, 104684265181630693852263659607784247353197338343165539, 452896057797041641977705935149835185059553347438117082, 1959366470330762621787100334040933024256883627575691183, 8476816918501136798284671505905721181113259880185081516, 36673295250202456112043947219425560907237714955731062439, 158659859878905047014528598709161455051551681088509778254, 686410941941597553858515593448109424834035380056754611491, 2969623076540957332872648829027717372995482123220310533566, 12847495105162390716791528895968284304744667558715421745735, 55582182055721606314415111576810995626089184602088683522960, 240465471034427887404152776028665675251117740259653486757099, 1040326964886707537783366221929215151535692259745294759052570, 4500771729157891263062785950262986547572051094483178822921049, 19471711146305731493232184404060025861319028294981859853489890, 84240560904008916778979940063794493598935110155820998433107117] The square roots of the the two last ratios (giving appx. to the "connective consts.") are: 2.079977159, 2.079977159 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (square-lattice) Self-Avoiding Polygons of width <= 5 equals [0, 1, 2, 7, 28, 124, 587, 2896, 14423, 71041, 345224, 1662744, 7970605, 38129599, 182302576, 871734302, 4169900463, 19952821632, 95493603031, 457080129451, 2187908704418, 10472951649460, 50130920791677, 239959375373481, 1148592957681560, 5497843321962449, 26315855791875398, 125962792977043459, 602930237765811160, 2885971051229262709, 13813922165623524524, 66121413853430255841, 316495333138632964768, 1514929813875040167836, 7251330846155965965691, 34709065950764713453608, 166137675114325514191927, 795231047396883744383903, 3806435927037194440842788, 18219804764796266668491367, 87210527558026643472027246, 417440044716439237262503403, 1998109584332621289004513612, 9564108577048601177739595936, 45779357453748372651887409635, 219126492789595193155564309541, 1048866181525900532555743039710, 5020480420991275699452947723741, 24030924155526704285718320401942, 115025907351392277190338189747680, 550580546810467966114692324793927, 2635397064058096572415069102262607, 12614535194640346761273546395364528, 60380464236983683092434097991826920, 289015838096160629917379646689057981, 1383397026273156750009699484327752660, 6621738604045329267933175332230197801, 31695472310242881305799277998506901762, 151712869540905663751097672033559593227, 726185574994546649774512758861864162438, 3475944334359771648033943185515974178373, 16637880772636623718511448907474604203814, 79638524089154262796716488540599681678855, 381196055301079632718406603674000465231889, 1824624881476079271460957783417393262192680, 8733710414374679776609384162699766987474465, 41804591385627566886920444721479752042045068, 200100962592359195284482569489637198590375674, 957798985786873084445821087021556159958816933, 4584580130397597431731003286704826554688856902, 21944453151377014675751930009395922630349303719, 105038849887267098428974674599677033648008445650, 502776711250492075551449418034813228592804425803, 2406580247662283690315410317994951215364038699581, 11519285517488436351952456552384421534545820479080, 55137965568493198529522593912901673953655009691490, 263922206148702084620296431135983655125602328936433, 1263284384547551213644677389310685820731724936912852, 6046810003332997274871446446177058056191474967448165, 28943531372394401988299569277005000838905099462123361, 138540487933807066162482907198629649230693996092137752, 663134935056458858216028577474041282549804754956949186, 3174147490388802747935979840450860047565331052065019649, 15193306457129630638110561968462113997840104751176813229, 72723955581528965162141375113690728310242963854944455256, 348098929640320730320449729077130269403972977779736845389, 1666202888000133121030682267335875506585541191674642412866, 7975411090314394800589505336090322842944463049053162338065, 38174932067159375714789645627512246068617549657264961397422, 182727312965980878301029001455113452940127675148290806988127, 874638646246372832981357606752950973326752769464069988773152, 4186526628616870631884952164132840113484101290198869269327537, 20039138777296883410423756517934251319144172655848344644852928, 95918912874186565679832438080469409587674657201726581899605222, 459123415891970653661650167429414260779992492856644231831421661, 2197630318191813419229462112563583113992231554673719055102128030, 10519130256192870504034241342449414607016969816980158056068636515, 50350643796084704496724794797134453986424255797100821906880618355, 241007314191938640001674390499837761560017655814470167939514780006, 1153600453039857950385118214299848923418918562703592646090860695285] The square roots of the the two last ratios (giving appx. to the "connective consts.") are: 2.187825085, 2.187825084 The first 100 coeffs. of the generating function (in the variable s), enumerating 2D (square-lattice) Self-Avoiding Polygons of width <= 6 equals [0, 1, 2, 7, 28, 124, 588, 2937, 15212, 80334, 425256, 2234664, 11636440, 60154100, 309445332, 1587239858, 8129416834, 41612899179, 212994849880, 1090396902150, 5583459055126, 28596711253568, 146486986471502, 750459222653252, 3844854716971816, 19698973131304193, 100927561148066290, 517099850430961289, 2649329982986918312, 13573589770972271487, 69542618665812625394, 356291763508908686123, 1825406569259453698768, 9352183017090740759274, 47914421019613104441372, 245481918875962489052517, 1257687821588800202806054, 6443566184091583124066710, 33012606006599101815623584, 169134957375015019579809135, 866536740193765196321210194, 4439566860275296546125921797, 22745433968024626798678197812, 116532712188913737406334029876, 597037320358966232498236041656, 3058828314770126074168179824626, 15671433403929637399354302512010, 80290162969641663941129352743421, 411354219232464974444446335195458, 2107509652106806670515690947870186, 10797499389043962200241932576449788, 55319316294721214748583738358410254, 283419951726914429068158617402085532, 1452058239903669298057365796583818338, 7439395566920882135475902257768931392, 38114591335306383955416012854010114319, 195274207390669154083384080141229726832, 1000457167143737415737439110065263527615, 5125687394614188328287020571246757228378, 26260665753970416959597716821643307754229, 134542455040386245704039690952138846905468, 689307437130263182798906646492537098392201, 3531559928334923317942024813246433053675186, 18093400499617316358379608329422573215051812, 92698736049149811389823651702086761236123886, 474927621553198587044723585359316470472280113, 2433218135728990457324584338803925483331843312, 12466216381931276821262068198081258631706564826, 63868729481817099530022079823924245557971246576, 327221546670288804297629455823677269564448695237, 1676468930477113478955289137778784081788258346706, 8589128996714368265273287227186266446630608378327, 44005072555214260585456608244568460079207287274384, 225453175907657919985239508820894730679800389349580, 1155074439726800821705002245680964723487161266371972, 5917845051145659888298402761273407657956159776608534, 30319162856423764709935657940184871332210681187434060, 155335536562651690797734989080735780576263773795436201, 795837570894359624865666670392933575655822337626512108, 4077350574519559098287363577967542995533032579763637530, 20889674370175857666016784782745808908863404038677213262, 107025012276115161898605237337103229968353909380390262132, 548326079656652741433336730997313438033762209972879200338, 2809263771500005622563977932987190611543593976871424120158, 14392827973464570818668791874935554218825220107387941076170, 73739425672775012625965340047726081788297022413927030501425, 377792530319656309530514100982726599973611961622287229065846, 1935561535272766457497064723955951455631021007275195373500549, 9916549841939917360665124131133081232164293219718659103905216, 50805907730451184564517618648316116283677048807122409087408233, 260296201951037282373615865662099282202593788972318115361603170, 1333587288895654831146379635089144446220606644743725680745502275, 6832427994622053686328348167695490652274836835990790904043635000, 35004886961957035387033199321964061244388634116992094236042757294, 179342118524173533579224115151209685195488745207026419761749138716, 918831576622252336063719037644265383747515806288808057574731568873, 4707491319638544711183639695765446174313316796724525115450409050892, 24118102912763526083468248417029324879577800950709579108567958652378, 123565366054740985702211297037136201950443551619244081946002244237596, 633068021289599674609345085024747242553496413883506079795457413779691] The square roots of the the two last ratios (giving appx. to the "connective consts.") are: 2.263480764, 2.263480764