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A186174 Number of (n+2)X5 0..5 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

%I A186174 #7 Jul 22 2025 10:18:02
%S A186174 143369699,6520730198,188034884094,4041778238254,69471558136868,
%T A186174 995828085723859,12251749347425002,132151619698400257,
%U A186174 1270399513311212137,11027904404610778911,87373338782676104482
%N A186174 Number of (n+2)X5 0..5 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.
%C A186174 Column 3 of A186180
%H A186174 R. H. Hardin, <a href="/A186174/b186174.txt">Table of n, a(n) for n = 1..200</a>
%F A186174 Empirical: a(n) = (5150863/824765059208247066672317030678549625218625855134543749292212313438895577497600000000000000)*n^65
%F A186174 + (295665757/25377386437176832820686677867032296160573103234909038439760378875042940846080000000000000)*n^64
%F A186174 + (1054942319/99130415770222003205807335418094906877238684511363431405313979980636487680000000000000)*n^63
%F A186174 + (577552110977/75527935824931050061567493651881833811229473913419757261191603794770657280000000000000)*n^62
%F A186174 + (59894488270867/12181925133053395171220563492239005453424108695712864074385742547543654400000000000000)*n^61
%F A186174 + (1065405880438153/399407381411586726925264376794721490276200285105339805717565329427660800000000000000)*n^60
%F A186174 + (486941503222193479/419377750482166063271527595634457564790010299360606796003443595899043840000000000000)*n^59
%F A186174 + (1148852947820574869/2843238986319769920484932851759034337559391860071910481379278616264704000000000000)*n^58
%F A186174 + (10188045327324139711/89129748787453602523038647390565339735404133544573996281482088284160000000000000)*n^57
%F A186174 + (219708279104561498399/8190703731512026965358605858782111420964456716711060644079389900800000000000000)*n^56
%F A186174 + (9001731634833500687/1692294159403311356479050797269031285323234858824599306627973120000000000000)*n^55
%F A186174 + (370777455676336370337619/409535186575601348267930292939105571048222835835553032203969495040000000000000)*n^54
%F A186174 + (74898466936227028440837965039/559015529675695840385724849861879104480824170915529888958418360729600000000000000)*n^53
%F A186174 + (28274949335272458543055008113/1622686588318420436533308707871927734342015009914455410619501772800000000000000)*n^52
%F A186174 + (32603865088220498306101326313/16226865883184204365333087078719277343420150099144554106195017728000000000000)*n^51
%F A186174 + (3762852653455603568852886589/18181362334099948868720545746464176295148627562066727289854361600000000000)*n^50
%F A186174 + (3679029326257728738103092261121/191977117813477720974067874341547203116476191649151778836971520000000000000)*n^49
%F A186174 + (14163560554708399992512066225920421/8830947419419975164807122219711171343357904815860981826500689920000000000000)*n^48
%F A186174 + (1464143223673179289410862286497292839/12012095523915579854856960564766218293181150073392721870819688448000000000000)*n^47
%F A186174 + (47488777224830909654253996066528116273/5622683011194526740571343243082059626595431949247657045915598848000000000000)*n^46
%F A186174 + (3272739201111321505043969743669429489121/6111611968689702978881894829437021333255904292660496789038694400000000000000)*n^45
%F A186174 + (3627767545668575645204268241995166825919/116411656546470532931083711036895644442969605574485653124546560000000000000)*n^44
%F A186174 + (1117281828746044765039482892057642362527203/669367025142205564353731338462149955547075232053292505466142720000000000000)*n^43
%F A186174 + (2567973397650330896056234759789982568539821/31133350006614212295522387835448835141724429397827558393774080000000000000)*n^42
%F A186174 + (320287479833639006904856419653509968149189619611/84994045518056799566776118790775319936907692256069234415003238400000000000000)*n^41
%F A186174 + (50855311823218513943609084869960596090112879013/318927000067755345466326899777768555110347813343599378667929600000000000000)*n^40
%F A186174 + (49905236294496839808811539757261137118535016607/7973175001693883636658172494444213877758695333589984466698240000000000000)*n^39
%F A186174 + (643404004194286193824255210767898657184723/2819456048125210251964363287210694771411313233202931302400000000000)*n^38
%F A186174 + (182958146578590323970212306808895850382428377/23650808998736267816064700301808720603161015964470870016000000000000)*n^37
%F A186174 + (25479232498485551017663204808529456459685599028457/104415125674150522912274832278390662446658161021522070732800000000000000)*n^36
%F A186174 + (24357416326993383863985022508874088194923562116020147/3398712340693599520794545790661616062638723141250543402352640000000000000)*n^35
%F A186174 + (78385500405346740828278350706261390631009686799139447/399848510669835237740534798901366595604555663676534517923840000000000000)*n^34
%F A186174 + (1358196804708022161354107892189107031012288010965021762559/271896987255487961663563663252929285011097851300043472188211200000000000000)*n^33
%F A186174 + (3070226171399452825069726768140620022729532271675710149337/25894951167189329682244158405040884286771223933337473541734400000000000000)*n^32
%F A186174 + (2736563737245402747193729435589388910352476086388670639/1044151256741505229122748322783906624466581610215220707328000000000000)*n^31
%F A186174 + (56315444637120277045048580407931063421765712716275439763/1044151256741505229122748322783906624466581610215220707328000000000000)*n^30
%F A186174 + (26762203926868041694821881286042188748147296057204827354631971/25912818755505121819139060606943695102715759834167449516769280000000000000)*n^29
%F A186174 + (5639778212017008405513161844646203252050881322382053427666773/306660576988226293717622019017085149144565205138076325642240000000000000)*n^28
%F A186174 + (59941586369317406072387198241278908743725648250974621705801/196965785614967481142741415376586311209453936106471948288000000000000)*n^27
%F A186174 + (22190324314147817272263261399037820781168355179984796905960787/4745937501008264069439388389550127308189699603327371706368000000000000)*n^26
%F A186174 + (162075405379116846812951443399048540540983566844061609714873823383/2432292969266735335587686549644440245447221046705277999513600000000000000)*n^25
%F A186174 + (856096408330166122407757063969139178767364417973710488246071694153/972917187706694134235074619857776098178888418682111199805440000000000000)*n^24
%F A186174 + (44926394300299884891964125438276895639255569314379951688375976569481/4177859744221476645720045293560463802030403325060886476881920000000000000)*n^23
%F A186174 + (2029626113584631445540682121163833550629278086687020017844153076750797/16711438976885906582880181174241855208121613300243545907527680000000000000)*n^22
%F A186174 + (608102515483472621693504165880721759237147293436627862486692061970772399/480453870585469814257805208759453337233496382382001944841420800000000000000)*n^21
%F A186174 + (9752624460540694582681270854673410850543891946580746346249460634104693/802763359374218570188479880968176002060979753353386708172800000000000000)*n^20
%F A186174 + (50550967839415448623880190339122689814208069638671219234627512315838477/471623473632353409985731930068803401210825605095114691051520000000000000)*n^19
%F A186174 + (1069220101559780580047192956449246313981084768433241778353045452188559/1233002545444061202577076941356348761335491778026443636736000000000000)*n^18
%F A186174 + (1854325300329358107464335436909610017994654640718671410090709828552832993/289008323909388284907081519436101747543334209182864894853120000000000000)*n^17
%F A186174 + (35282841137245027885183445602188464706613704124606545280588170014057079539/815151682821351572814845311230030569994019564361926626508800000000000000)*n^16
%F A186174 + (1351643389034485586593280994460593703327473572822720227971199214007035893/5094698017633447330092783195187691062462622277262041415680000000000000)*n^15
%F A186174 + (59505814592641625426033996831123198617661961960948861403311297104176033/40434111251059105794387168215775325892560494263984455680000000000000)*n^14
%F A186174 + (1231306464849732692867522600936686835934491043125526785020908888596257537/167422491898916609929884368393444708773883296561810636800000000000000)*n^13
%F A186174 + (4901472324532061393740852302931001246613714686868051753966469067961737171/148819992799036986604341660794173074465674041388276121600000000000000)*n^12
%F A186174 + (270810676109354525078196296256955162276398139747994873895771335717263783/2061776983569991585247650092252606135826525781733408768000000000000)*n^11
%F A186174 + (1272674740404878067341944690768786629628722465089955868837232807100683671/2749035978093322113663533456336808181102034375644545024000000000000)*n^10
%F A186174 + (569520041768279902455986116881394651831083959323747340263939036507691381/398610216823531706481212351168837186259794984468459028480000000000)*n^9
%F A186174 + (48295063166291073729892338083645778295649967038421694053810793531470911/12654292597572435126387693687899593214596666173601873920000000000)*n^8
%F A186174 + (21080675759219251726353144113452648847922189047643637756295010944681/2424036569015498936548291972682064933964945792995164160000000)*n^7
%F A186174 + (179202547860022006349424507439977911747018812665939606970955064137/10797053068987078191622615686549527969555557063065600000000)*n^6
%F A186174 + (10379513418673040616220953148745067856482452395581979697751706241/400700416055116762054134603596689381152754014615552000000)*n^5
%F A186174 + (130723978690483584547632515779889902216295144355286616495611211/4091956740711593085689908261837653797985721982976000000)*n^4
%F A186174 + (116995296197082949816186044174315062498902211108276373719/3974316958733093517569840969150790402084034560000)*n^3
%F A186174 + (164677504535476949980363690870238723165973925051/8985449396468081909874568086555575040000)*n^2
%F A186174 + (326401271208523397722560632043637/51402908004470533370059200)*n
%F A186174 + 229362
%e A186174 Some solutions for 4X5
%e A186174 ..0..0..0..0..0....0..0..0..0..2....0..0..0..0..3....0..0..0..0..0
%e A186174 ..0..0..0..0..0....0..0..0..0..2....0..0..0..1..3....0..0..0..1..4
%e A186174 ..0..0..0..2..5....0..0..0..4..2....0..0..0..3..0....0..0..0..3..2
%e A186174 ..0..0..3..1..5....0..0..3..1..5....0..0..3..1..2....0..0..0..4..4
%K A186174 nonn
%O A186174 1,1
%A A186174 _R. H. Hardin_ Feb 13 2011