Squares in Squares: s(n^2-n-1)

This is a list of $s(n^2\!-\!n\!-\!1)$ packings (a pattern found by Joe DeVincentis in April 2014), shown alongside any packings that may beat them in optimality. For the main list, see Squares in Squares.

Where the word "alternative" is used, this designates an alternative packing, which is enclosed within the same-sized bounding square as another packing, but cannot be reached by continuously translating and/or rotating the squares in that packing. When the packing can be reached by such continuous transformations, the word "rearrangement" is used. For more information on each packing, view its SVG's source code.

For odd $n$, there is a predictable ordered $s(n^2\!-\!n\!-\!1)$ pattern that continues to infinity. For even $n$, the optimal packing tends to be chaotic and unorderly.

$s = 1$
Trivial.

$s = 2 + { 1\over 2}\sqrt 2 = \Nn{2.70710678118654}$
Rigid.
Proved by Frits Göbel
in early 1979.

11.
$s = 2 + {4\over 3}\sqrt 2 = \Nn{3.88561808316412}$ Found by Pertti Hämäläinen in 1980. Didn't set an overall record, but proved by Walter R. Stromquist in 2002 to be the optimal 45° packing.		$s = {}^{8}🔒 = \Nn{3.87708359002281}$ $s^8 - 20s^7 + 178s^6 - 842s^5 + 1923s^4 - 496s^3 - 6754s^2 + 12420s -6865 = 0$ Rigid. Found by Walter Trump in 1979.

19.
$s = {}^{4}🔒 = \Nn{4.88810889245683}$ $s^4-12s^3+51s^2-72s-36=0$ Found by Walter R. Stromquist in 1984. Not optimal, and didn't set a record.		$s = 3 +{4\over 3}\sqrt 2 = \Nn{4.88561808316412}$ Found by Robert Wainwright in late 1979. Beats the $s(n^2\!-\!n\!-\!1)$ pattern.

29.

$s = \Nn{5.93434180499654}$
Found by Thierry Gensane
and Philippe Ryckelynck
in April 2004.

41.

$s = {}^{4}🔒 = \Nn{6.93786550630255}$ $s^4-16s^3+95s^2-218s-34=0$
Found by Joe DeVincentis
in April 2014.

55.
$s = \Nn{7.9547901}$ Found by Joe DeVincentis in April 2014.		$s = \Nn{7.95424222760119}$ Improved by David Ellsworth in June 2023.		$s = \Nn{7.95421084599443}$ Improved by David W. Cantrell in August 2023.		$s = \Nn{7.95419161110664}$ Improved by David Ellsworth in November 2024.

71.
$s = {}^{4}🔒 = \Nn{8.96028765944389}$ $s^4-20s^3+151s^2-468s+12=0$ Found by Joe DeVincentis in April 2014.		$s = {}^{4}🔒 = \Nn{8.96028765944389}$ $s^4-20s^3+151s^2-468s+12=0$ Rearrangement with minimal rotated squares.

89.
A continuation of the pattern may exist for $s(89)$, but is unlikely to be optimal.		$s = 5 + {7\over 2}\sqrt 2 = \Nn{9.94974746830583}$ Found by Evert Stenlund in 1980, by extending a pattern found by Frits Göbel in early 1979. Likely beats the $s(n^2\!-\!n\!-\!1)$ pattern. Explore group

109.
$s = {}^{4}🔒 = \Nn{10.97240394480333}$ $s^4-24s^3+219s^2-846s+126=0$ Continues the pattern, but is not optimal.		$s = 6 + {7\over 2}\sqrt 2 = \Nn{10.94974746830583}$ Extends a pattern found by Frits Göbel in early 1979. Beats the $s(n^2\!-\!n\!-\!1)$ pattern.

131.
$s = \Nn{11.97614140898726}$ Found by Károly Hajba in November 2024. Doesn't beat an optimized $s(n^2\!-\!n\!-\!1)$ pattern.		$s = \Nn{11.97350182495032}$ Found by David Ellsworth in November 2024.

155.

$s = {}^{4}🔒 = \Nn{12.97970624703929}$ $s^4-28s^3+299s^2-1376s+332=0$

181.				182.				181.
A continuation of the pattern for $s(181)$ may exist, but might not be optimal.		$s = \Nn{13.99404229036268}$ Adds an "L" to the $s(156)$ found by M.Z. Arslanov, S.A. Mustafin, and Z.K. Shangitbayev in March 2019.		$s = \Nn{13.98318264138415}$ Found by M.Z. Arslanov, S.A. Mustafin, and Z.K. Shangitbayev in March 2019. Shows $s(n^2-n)<n$ for $n=14$.		$s = {}^{66}🔒 = \Nn{13.98264294789927}$ $1713850177070388831714241s^{66}-923663845843030533029467964s^{65}+244356526675459843171256658812s^{64}-42301149163464927098830722044712s^{63}+5389637680061232065659444372903884s^{62}-538990344040466547260756897354234800s^{61}+44060430495129161810848298418942728768s^{60}-3027597018002804743276382310802134926912s^{59}+178476725866222249279843650493042891414174s^{58}-9167125837455703044437102107796599060405072s^{57}+415277865358575078055753826628996914179647584s^{56}-16755219749633813087434458219665047861571005696s^{55}+606951588795740859789587928711977301863618562444s^{54}-19872617896564458386479749674438181110594571783440s^{53}+591430450596695946776559043737897061925817091883896s^{52}-16076403382596088035670122941655178909884706102259360s^{51}+400780790911848317908826372889780636781368953842134545s^{50}-9196292015835695622526434508695387052579786474968530764s^{49}+194831950657120243957930949495672896263326187482945017636s^{48}-3821488517527886494201924904813013938910357960132992875112s^{47}+69561259675051249201492552497458936188600783387550785194512s^{46}-1177541097875302951212548144402084258394462103241418878091904s^{45}+18572022118855878686507143350115259541331165972203297602035016s^{44}-273350438905317141283665359004770430754125267452024933490938688s^{43}+3759875778293105916627657039864999051693799407851712882736113208s^{42}-48390183666058035250293916819527929345794012592770993441540548200s^{41}+583359495992769368180893839833879135938973736557186058881098499424s^{40}-6593404023892398478887639745053689330072639258527396503597740822704s^{39}+69922254584057803430223785412744087886168418412416437299744434763920s^{38}-696199801753965501285725548974198631608011266843672974698091490432160s^{37}+6511650429478482167950610493981767940220071476762446758258297829362464s^{36}-57234890555844218227733552885344124231228022552073037991205841355754784s^{35}+472897245542288005015724033828084119792469894384102779109267997968480096s^{34}-3673527397539404818977007733654565672521620497606425069188768378430791392s^{33}+26830967247160316756709981320435477112019319138841629014760220636370474816s^{32}-184248363314616695085417127987503784871627748574838179238693969981716890752s^{31}+1189362835357759435647680170936163404089852639152762150758843550851500029312s^{30}-7215198553515381078457422107373261572387237955159216402793836179726031898368s^{29}+41118237990763833027717928080095280450530652728789049212131791394290259869888s^{28}-220013586830299858346544628394840804319064288631784649846740295442808772668160s^{27}+1104624680933328901706883047576578922329679532689002041544873488282388304886016s^{26}-5199881073657329493566722212089680068736612815975219398932756978414737762064896s^{25}+22929072742861089738590065098448598702132646005025936214483918913337650353069824s^{24}-94608008640637296299957783267672779275948371642923398380136113133454728406140416s^{23}+364819925689129881972579265818449668453976797240020471862122424163060417660220928s^{22}-1312862171184299432821030617749268935136513935049032859605965972625387377719365120s^{21}+4401912097721267325119409154299200433015462297229066215750087595154529481296731136s^{20}-13725788367315319506315635643739707608001009560356143859397586956998117539703622656s^{19}+39717900153429166873869781810993511500356117237564376538643805576134915824234523648s^{18}-106399332388497647615120413383665293526457978124604308307567938191333861608693833728s^{17}+263146214957976354333140167648787212861652057702279153736060651315259635818278014976s^{16}-598948423050050797962529487281503994476619892474808687630034845197011146318218905600s^{15}+1250084500161595434165407078512122830805401588230922174957693497088606844442474217472s^{14}-2382458928043568775151925441566626859323222839887782280481843477807775050701314756608s^{13}+4125994826986881535378038074633666561772029457781662960093867812493907378777176526848s^{12}-6456003870217606716135295888226937623998759028219550792812724057683607497186984583168s^{11}+9065372956178732821827510381589091533382082905889742319984764707994104046708843806720s^{10}-11330803663084115039545790076138860721501300902182053330467921505356766127529332162560s^9+12481974955426380241965795213639280113780047248776326121594789973305180053750293086208s^8-11970325319419753577043006848391910395086707654239813304187044220003154526297518047232s^7+9838402392037009878211651167751684462461327699694726737875855220251210658084493393920s^6-6789017987208597545069669454098514525060401317357596876693764512756899474772483768320s^5+3824088158296275561318991814461422505555214264984822149493993857503600579756629164032s^4-1687927982575032415641479063772412094421237083850884119669396632875631662093020692480s^3+547314545007055176499085872328704154179592545295820829835019843713968328240803086336s^2-115875113076825478429958642319077276340668682757823451130118465600944508946094227456s+12012260314488957307342435041239878634388761717780836316682092965799623955237044224=0$ Improved by David Ellsworth in December 2024.		$s = \Nn{13.97854770217285}$ Found by David Ellsworth in December 2024, by removing 1 square. Might beat the $s(n^2\!-\!n\!-\!1)$ pattern.

209.		210.				209.
$s = {}^{4}🔒 = \Nn{14.98444916984191}$ $s^4-32s^3+391s^2-2082s+654=0$ Continues the pattern, but is not optimal.		$s = \Nn{14.98318264138415}$ Found by M.Z. Arslanov, S.A. Mustafin, and Z.K. Shangitbayev in March 2019. Shows $s(n^2-n)<n$ for $n=15$. Beats the $s(n^2\!-\!n\!-\!1)$ pattern.		$s = {}^{66}🔒 = \Nn{14.98264294789927}$ $1713850177070388831714241s^{66}-1036777957529676195922607870s^{65}+308070885285072811862199123417s^{64}-59939613454150601563431685241960s^{63}+8588813678023291261040553534326772s^{62}-966583568773741127569549391339079520s^{61}+88973510619748651618414859862026730876s^{60}-6888549315978477501144600760825939298456s^{59}+457813058489637019372876565898875762561962s^{58}-26525924226609242481987455544648574755740060s^{57}+1356297999041102109336083334683724973134359610s^{56}-61799914557147552310687442895919575623521766840s^{55}+2529586572366492011492859050137381026019860276228s^{54}-93635049365714878103413599709118844924967191715568s^{53}+3152090707330317380212505369273541211594578660668828s^{52}-96964556710709267169581794961613905049794026876686584s^{51}+2736977327538183203599671149196691182209406477480426999s^{50}-71141341918871267999443622612794042553629895963414923554s^{49}+1708099525395866416691912276683615496482061285927149098767s^{48}-37985865900286624496819504298337826100292397570681660970624s^{47}+784296971154264745366602352186813069922416329570936529960120s^{46}-15065885306353527422811618762658136922751746094197077043607808s^{45}+269749236797310845207931452385959355761508726043413698724913752s^{44}-4508953939245292278547355693056226796525821395294109220913219760s^{43}+70461706096440343504339359622207886316103484007784533453402451564s^{42}-1030684846592380569306994628265946835298274035988655898515756518536s^{41}+14127213285791424916401341828825119374306871082227591450747564708428s^{40}-181611012865775124333222503250168271689890578495810300493810490865200s^{39}+2191389437227659168703888781115852382017210534407970049772895556135144s^{38}-24835252575107480313771638509524748878675003716854534342036362523912096s^{37}+264493817830994381831108752939852505433266002142853663596745464038105112s^{36}-2648106506791820424837514470078773670571332661118776845107705934142835760s^{35}+24931817840154101718618675302330328982025705361265314835179979339556004095s^{34}-220774232592783180535637731350600608019775280385941635854721272379834520226s^{33}+1838859783489983364796248010427404448952293664994580697429468489690817448391s^{32}-14405793276814386692861915917557813798574320839280787544681770605702716243496s^{31}+106132652991766969969790599313795738256162256172065649640195937493783785627012s^{30}-735141103620029965659773734189613183265405874983552791121595763935147775210784s^{29}+4785629939469775130214760518204470967279654407141021153131677479220692014706252s^{28}-29264396180717787590970697217467423077531807932966908615153820237900145532452792s^{27}+167997715129752800946484031210802390736511802747887658272905155103288606648529418s^{26}-904700154474475752208581796921737926689902979381082659180178913034340167719783580s^{25}+4566216117618812719619282953953565095633492925168145038704985120782850946704225818s^{24}-21577735591142156619368360651289725338415069076557628274035844600998082681026841624s^{23}+95351638011084223101955380792874473279508189366232625045913569058491535016623736724s^{22}-393477264331394419045246438963291356261882874125326625922439475690536334420518557680s^{21}+1513871326020646900995786895290089433666501518786395002635104303984667876045713548492s^{20}-5420589319604280486120080489351603688574661016232355428256686514216840385980014845144s^{19}+18025671901154216272856257915455921861722569907273247804240829505876591992203422527785s^{18}-55538726517617123321306980401388416698101944528011997777048904298548850658621880672382s^{17}+158119388173030536226827428726717197786937874399240446800307626931688853687437117891505s^{16}-414679766978138921331059461345942561913790083283653894727325899938505427858892965125872s^{15}+998228943688800328823203749490058494562116495933106174279441691815211346156075844428112s^{14}-2196572339864925849617348696491086772493215350378298856026223386996595289374884651752448s^{13}+4397165113585946993607002307549324635278671461053934532945038939803841295777334091620192s^{12}-7962739349659864081806356456004225116652369166110620089333680683881143975151724678690048s^{11}+12957137888727586584941034560243767737163859971700725359751881246527790566047851156973568s^{10}-18794133216992559109409136095289044747144304027555381568607235733444082266478813293896192s^9+24062707252931451750084904210379578567640678822720136431418887027294986269907390293532928s^8-26864643906507885513435835499475292614570149380412717542767363827389611363117057750564864s^7+25750555425531123093287716207567520607853292058501569356839679301847154190381313748566016s^6-20763167580966447999929009292788490161886160932306769296176687436564687869505524614365184s^5+13694576920953853335160219343243224031929703522356095792630808590038480485959704606801920s^4-7094101031359142126885338736264230663456345418028425142721873216376995826523389107896320s^3+2706320051143905447935556673344831161461373449684695751208915990592616770507314550538240s^2-675931907390084983300050927121665770468081954992407462935298185140040600624082498617344s+82905798822484597710700208785408047898314652058813563312936555293758738816713843802112=0$ Improved by David Ellsworth in December 2024.		$s = \Nn{14.96442179744201}$ Found by David Ellsworth in December 2024, by removing 1 square from the $s(210)$ found by M.Z. Arslanov, S.A. Mustafin, and Z.K. Shangitbayev in March 2019 and improved by David Ellsworth in December 2024.

239.				240.
A continuation of the pattern for $s(239)$ may exist, but might not be optimal.		$s = \Nn{15.98318264138415}$ Adds an "L" to the $s(210)$ found by M.Z. Arslanov, S.A. Mustafin, and Z.K. Shangitbayev in March 2019.		$s = \Nn{15.98318264138415}$ Based on the $s(210)$ found by M.Z. Arslanov, S.A. Mustafin, and Z.K. Shangitbayev in March 2019.		$s = {}^{66}🔒 = \Nn{15.98264294789927}$ $1713850177070388831714241s^{66}-1149892069216321858815747776s^{65}+379137661154317748641195681912s^{64}-81891074048159729003070697178408s^{63}+13032601897654000375127635736914044s^{62}-1629704803955659741528480932743629600s^{61}+166761277204901256215813369062945614448s^{60}-14358776608758577299719024788683561291200s^{59}+1061744286766486909447032265740305813536222s^{58}-68474327034163224324683196882521071680487400s^{57}+3898680014040310378546424786982864974691587032s^{56}-197893479763233829851953449206470703678382928256s^{55}+9027058972990094483551124675146985797402686345676s^{54}-372525707164344655382696831764231550931861454524704s^{53}+13986254561093171332246318032879802874415524621400936s^{52}-480021129624779505518793563427218381659637764171707744s^{51}+15122329258714384953594013673578917012766694983733804881s^{50}-438855029419115553162393305979405927798765869173444577904s^{49}+11768226418611255713545406862693986409497534694395932490528s^{48}-292389611865138370972616101847672913969792672213028811518184s^{47}+6746862076174715126011529791080074820752050442542414504370560s^{46}-144888150698948224043410517981223612722489152566776581298794208s^{45}+2900996894928148652325377674448953709338108189036698898804529608s^{44}-54242556288254952045704327412146319996536264265171980175919237760s^{43}+948462355395453479168602938292256298703061926500378052173528780792s^{42}-15528080343980828527604766556375005181552902663086802848142696321224s^{41}+238282964650245168300609610231809513127916963399478723451985201685904s^{40}-3430367236060179440070732218664376912627362282540244578551905978189104s^{39}+46365532467244547446360743216142017095989148306459526039623515846047792s^{38}-588755762949838005565806711016983484397068959152714283441733945344802848s^{37}+7027249712549848127431398466867724250461309354203649153646258736184974752s^{36}-78871493856005778995281528812829746466339050516177676306484461418414160416s^{35}+832653557924952811014500182820751911383034261282044436164334245143830456352s^{34}-8269810361173954931078914169946911637391596761131737508844305945597487794144s^{33}+77275880265085319916055821144235805497262635145714014287742658219786671877504s^{32}-679349084345154135379649690958316686561437063246031516423762907925538312289408s^{31}+5617964001822564205130667238529394632220025771132883175722208150517560549227648s^{30}-43690824350734077930796967911338231155740749007361979222513577735261402688590592s^{29}+319422913565064992742490317937286445800967315990365504365040042142459301153592512s^{28}-2194292900885520709718961937109526038033002419198710908780183901772626370705331456s^{27}+14155019838518846812037482168797435038238593984348815057869321629794699529203855616s^{26}-85682417222445926795565973572329420277366975422152054005379234967639143358197815808s^{25}+486245607801686576677241553060465905470056389505993650262344015281342122162160575232s^{24}-2584368483713735021047686463913913640136052794643430856590242035633830225424725988864s^{23}+12848980595866502714148654836356043391589862545760566610324380590058932864681066715648s^{22}-59676137078910398640252148320907121417908906930343892171666836705986652465992239468032s^{21}+258503073948652279571122377723799998795218261647593540516168322657994235939676499460096s^{20}-1042512327688912764291535477319351885866939675291965746264513281156719001472917009644544s^{19}+3906196167448619261818676733246713157402634575850720548507828059644983940218233231610880s^{18}-13566400556764072761657734569104915733372068338209863555592826673337289078412816532291584s^{17}+43555912849470441098868802000969681226084842115362413993508512687803571381115014140829696s^{16}-128873854467322076750495059627569588067583487401622277235861210691551499032718516262586368s^{15}+350170085209767527530821777446058436886835554296012946187110660487759175384250607478042624s^{14}-870180189847506227220609230477835558202475594829635350625252034102067479987046653583601664s^{13}+1968252700727960939216791826879252136521049007411500029477449576057390685915953096594960384s^{12}-4029555319153116978053280766009889585799476763772621260420608643127295976220742724892581888s^{11}+7417299288136909883224183664841980102926026482386873232431581240176756976673835812755652608s^{10}-12177862422215869003301230978568940238954188047906715505518821155614152635401370021975375872s^9+17659998109675690653749221764562831419249106682956363249429630212164222854382762578641272832s^8-22347378432178696652088994803216423167402716129816166966820581562620109814623380610932342784s^7+24296916754024602064906452756050319984681043769067192580115816651405229556935324316920250368s^6-22239046622093583453544338095037087546806112181982198692585543077930687627404701078594387968s^5+16664365087788761186074795638291069350851003090434486799819196634836845588756587148389384192s^4-9816056457754695102925029410241846551198661538424486286292785393106187869550293083972698112s^3+4262107623285338836956260105382884155349919936507235251826717599203646332610595428224729088s^2-121279084664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Converted by David Ellsworth in December 2024, from the $s(210)$ improved by David Ellsworth in December 2024. Is likely to beat the $s(n^2\!-\!n\!-\!1)$ pattern.

271.						272.
$s = {}^{4}🔒 = \Nn{16.98770404979942}$ $s^4-36s^3+495s^2-2988s+1116=0$ Continues the pattern, but is not optimal.		$s = \Nn{16.98470216018343}$ Adds an "L" to the $s(240)$ found by Károly Hajba in September 2015. Beats the $s(n^2\!-\!n\!-\!1)$ pattern.		$s = \Nn{16.98318264138415}$ Adds an "L" to the $s(240)$ based on the $s(210)$ found by M.Z. Arslanov, S.A. Mustafin, and Z.K. Shangitbayev in March 2019.		$s = \Nn{16.98318264138415}$ Based on the $s(210)$ found by M.Z. Arslanov, S.A. Mustafin, and Z.K. Shangitbayev in March 2019.		$s = {}^{66}🔒 = \Nn{16.98264294789927}$ $1713850177070388831714241s^{66}-1263006180902967521708887682s^{65}+457556854283194653508246334297s^{64}-108626085650108755375383219863016s^{63}+19007543579258154993013605104517540s^{62}-2614249620222774694075991845075567408s^{61}+294320445544799712214422954346585080428s^{60}-27891472736856262183567432641837740604344s^{59}+2270607650860185114208141699776485160991834s^{58}-161270542469096575205017999202879333703379396s^{57}+10115431614750251067098547571363673856667344506s^{56}-565808816641730403858512432034552952494802469080s^{55}+28450183984319404845113532374059123476095944389108s^{54}-1294559647452187836265838445107719695018437168558336s^{53}+53606558683243577767537060160465091965389251586245100s^{52}-2029777274949400008320972989373569605256603237798407896s^{51}+70566124724622022053181378677212143452798761833741049255s^{50}-2260494118677599144499162628207117877734197301937499627454s^{49}+66928391584632217881721045867244937443110647589022537806159s^{48}-1836487293516144718606242405600092685339691196348395055392352s^{47}+46812433957159983606351028994995744914840143394813517611414488s^{46}-1110784325503673809119053441923324973802716059719307513683034144s^{45}+24580067642598124655873296327812538035270416503768622579007969464s^{44}-508058601195291180778593698054098715271789503226858668644025004528s^{43}+9822636844453945473008973446300398331806350662367666559112039098828s^{42}-177850157754818541348101942178417197242325906137100400008326274953784s^{41}+3018908592957234274621453725329581711584511453209430776141062678498508s^{40}-48084823616106717807937793455351705691203975334728299955852985477677936s^{39}+719219081331785321193765357384648827974404178174478952936526177053613640s^{38}-10108484874977669848442591400277761623042675059618304149046369427119689280s^{37}+133569141781888512562398911029947506237982901071358900752904689441632946104s^{36}-1659947237436600687047903428474338638444186680114020006663182877218281431536s^{35}+19407721788005616167841988847134491979124178917074454947061592816288392155103s^{34}-213512563646549268743663877471869657452486579360256542887702449445267477625758s^{33}+2210398398130635465592076383059864672001655782088693299537565902349619712869319s^{32}-21532723313632709226861394724764610661805015535470154323486739829302573530834280s^{31}+197353488882411915369080553242112202824443643000941071851504553934557696342479860s^{30}-1701361607748327036898500039362885770951773534397536787240248737455726000275481776s^{29}+13790944656640719079864365329065256075236685711621827154509298129212864382169075708s^{28}-105057191253365590055038856706594446361850240187411125808555225806066647805699033432s^{27}+751670513866794149869446078936059679095796755093931999846310783101254874128343844858s^{26}-5047524051032968924904168688747563678450991211248789313855857351391502072525065835844s^{25}+31783178768787466515646386129275724683780750656572320239619905303340921614133673928026s^{24}-187472727052955447696160431653518028007026362437178333588607245141115925448495562239416s^{23}+1034626229621705034003065868277725184320524563387572538925459708898162378122695884371524s^{22}-5335045699393078934531764329130636548870723955424210927081461414593591826916976872572736s^{21}+25663737575409659302307158237342619977251070651367656518135022159442843909863332058148316s^{20}-114960649295229282113311852806854796874367423592350138710159368893751322473994310949804856s^{19}+478559753673706084748519492363770439999236334487313334845093021068854656585876271428583577s^{18}-1846990700033721376192730686948971722144142619617398680320187325046521383970748784637316834s^{17}+6591326456994561029578640106261265890282504157582308701300923406400578110653255439076001265s^{16}-21683429758094255971784837646080964873309338986609460623022430958540451763873664347265934416s^{15}+65523328529399452484083881848848270952170741513603155833639414320711386575541360843917428752s^{14}-181134395473848110073827498749917703659200447864218040383057641661298047344658812692009492864s^{13}+455904206381436590247441608773490326831830404955375957062019998388748856279690733152466535776s^{12}-1038920953582196812525580854613110667241159361649685005599580196703726210365369892962261589248s^{11}+2129321555265993058808909413739742507947670301867618671926711075672095702442458870941704884224s^{10}-3893858393082444876460677140167356642408686917745920213899715750218779803640863536637271852544s^9+6291634657144980094912045673643258772753140381469197256391134629731334665393467914754165776640s^8-8874016200990822056453884612581892989147523385532622735339375442773419838200440294959402524672s^7+10757961171340950446264308166124992160748835994596014475038180685505768156638580567927181983744s^6-10983792379878536403573363876927768332193956898933674258258398402852665358347513825072163651584s^5+9184651747912342152838771898129517117129618056068600195075502388329608767166607606008661409792s^4-6040013853226973048374847053430821660325834738741764444484502435456762249243146187494035292160s^3+292921169504218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Improved by David Ellsworth in December 2024.