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A186175 Number of (n+2)X6 0..5 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

%I A186175 #7 Jul 22 2025 10:18:10
%S A186175 1662436696,105970767207,4041778238254,111203560772547,
%T A186175 2391923493659465,42174821764604242,629512200937395977,
%U A186175 8143852416376007571,92981285763140685886,950506396177707075676,8802483321307673371982
%N A186175 Number of (n+2)X6 0..5 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.
%C A186175 Column 4 of A186180
%H A186175 R. H. Hardin, <a href="/A186175/b186175.txt">Table of n, a(n) for n = 1..200</a>
%F A186175 Empirical: a(n) = (39140173/3055758079073951988794077480022729269504831158812863739172286445058165709895368704000000000000000)*n^70
%F A186175 + (4382389591529/171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000)*n^69
%F A186175 + (186759106340383/7440106627310491798802971255707514743142197604066103017115132214054664337136549888000000000000000)*n^68
%F A186175 + (7038713695025099/437653331018264223458998309159265573126011623768594295124419542003215549243326464000000000000000)*n^67
%F A186175 + (50311638919791527/6532139268929316768044750882974113031731516772665586494394321522436052973780992000000000000000)*n^66
%F A186175 + (81570446177838439/26992311028633540363821284640388896825336846168039613613199675712545673445376000000000000000)*n^65
%F A186175 + (2963287994018296403/2854955974182393692327251260041133318064474113927266824473042623442330845184000000000000000)*n^64
%F A186175 + (80251357206391596917/248257041233251625419760979134011592875171662080631897780264575951507030016000000000000000)*n^63
%F A186175 + (5510013991549935796007/60104336298576709312152658106129122485567876082679301567853528914575386214400000000000000)*n^62
%F A186175 + (783219350102795781554257/33489219638503151816155440000482502264685913359850637237220441330701828096000000000000000)*n^61
%F A186175 + (352056741551390883547971913/66429435676375104422209971148498078262737631418720116486945465590408544256000000000000000)*n^60
%F A186175 + (70406446001868025386767319973/66429435676375104422209971148498078262737631418720116486945465590408544256000000000000000)*n^59
%F A186175 + (304029178687758617544379169477/1626332700174908394517381591206167641083972143961132795348947368503410688000000000000000)*n^58
%F A186175 + (8762976309761536067897148601/300430917519995393075870983597198455865265790140603348894509981866393600000000000000)*n^57
%F A186175 + (17907583311726245214273248788543/4427402995031511055854940810906082507488127433650996720550673416978432000000000000000)*n^56
%F A186175 + (201686204169375815466694155525953/402491181366501005077721891900552955226193403059181520050061219725312000000000000000)*n^55
%F A186175 + (381467156922859614853583608476226717/6842350083230517086321272162309400238845287852006085840851040735330304000000000000000)*n^54
%F A186175 + (153199405873833646590919263711484533913/27369400332922068345285088649237600955381151408024343363404162941321216000000000000000)*n^53
%F A186175 + (7441331551635715910177888829877736299/14607948115328975098845920249136600538009510091833770979109858023833600000000000000)*n^52
%F A186175 + (9287647134941215894059004900232351057/220148950692852808976287568168806327991392714072361157196113562828800000000000000)*n^51
%F A186175 + (95408626463072637295351368934684280420321/29899821772672151913003954411498083934341194125542112268166035931136000000000000000)*n^50
%F A186175 + (564391789939555965375644149679770622795333/2552423809862256870622288791225446189516931205838960803380027457536000000000000000)*n^49
%F A186175 + (16942485895401420877288842780966831254562793717/1203467826350054114498409165062797878357233063553070018793682946228224000000000000000)*n^48
%F A186175 + (26852884612224645977213596950009421126435648291/32526157468920381472929977434129672388033326041974865372802241789952000000000000000)*n^47
%F A186175 + (646852543128830871460457008750369404156094823921/14472786070814711830230637507693221478856641837363469236186751434752000000000000000)*n^46
%F A186175 + (5889699094273188398816894092962689334766103014313/2631415649239038514587388637762403905246662152247903497488500260864000000000000000)*n^45
%F A186175 + (14385690197002531039842646743709628806553094011711/138495560486265184978283612513810731855087481697258078815184224256000000000000000)*n^44
%F A186175 + (287167882017259136193037454380715419873121784765889/64180869493635085721643625311278144030406393957265938963134152704000000000000000)*n^43
%F A186175 + (101743822584474801468110656038946092250517429339501/567896214533448311985371315312444377690442436578152196667285637693440000000000)*n^42
%F A186175 + (377709694131311449212944379523672421110326293324671/56568776948139295389337159261487590216837709240938595390324736000000000000000)*n^41
%F A186175 + (43877950974914355674444229921704827560964110890670077491/189232146220201956678990402714141194489173771569291255338829348864000000000000000)*n^40
%F A186175 + (1421263432381084002911751811533080115764984234409751502711/189232146220201956678990402714141194489173771569291255338829348864000000000000000)*n^39
%F A186175 + (19226174505278927265349400796789612200380472060936525443427/84656486466932454303758864372115797534630371491525035283160498176000000000000000)*n^38
%F A186175 + (347578096741760411447592549881682112737458777432916096519329/54180151338836770754405673198154110422163437754576022581222718832640000000000000)*n^37
%F A186175 + (6200578125954548971385218635534213556832690751916480772728181/36608210364078899158382211620374398933894214699037853095420755968000000000000000)*n^36
%F A186175 + (818579412735899982454245996637124506548885398822338830192203/195765830823951332397765837542109085207990452936031299975512064000000000000000)*n^35
%F A186175 + (518174343383783930756796030078238936435362176147716183747769610157/5367311783700273680349545967892004789147474248147170151428614258688000000000000000)*n^34
%F A186175 + (5594870528317629062340992164790800836627002916641028386951528357321/2683655891850136840174772983946002394573737124073585075714307129344000000000000000)*n^33
%F A186175 + (5649428414152825023800332915872847922342645113809721174371767802547/134182794592506842008738649197300119728686856203679253785715356467200000000000000)*n^32
%F A186175 + (19550333230779503953465217535972392575728498897098184450485788787/24593620709770315617437435703317470624759321151700742995915571200000000000000)*n^31
%F A186175 + (17113380352603225981693764255065586076762701510698922102149129621926339/1220089523411705357781071185241579717694309922335873860027371487232000000000000000)*n^30
%F A186175 + (4862391462382410545238761715134347913969077642112573682601602685060879/21036026265719057892777089400716891684384653833377135517713301504000000000000000)*n^29
%F A186175 + (61839241700066986712672895961618526372500876529208055459837752647693861/17395175565883067103642593158285121969779617592984938985801383936000000000000000)*n^28
%F A186175 + (6207766853428918935265626663066068173547109723951461342444061701830051427/121766228961181469725498152107995853788457323150894572900609687552000000000000000)*n^27
%F A186175 + (100384582694067594058743171073182989043917268793754396474186618472543697939/147401224531956515983497763078100244059711496445819746142843305984000000000000000)*n^26
%F A186175 + (1077568143207435118310546323194844233300283270291463803642809650623526126767/127301057550326081985748068112904756233387201475935235305182855168000000000000000)*n^25
%F A186175 + (6358307591436941997380318593178284624769340218676708108283375464654899385451/65034235922449194057936513057679603727926070319227783253734719488000000000000000)*n^24
%F A186175 + (8518666644737976457638142658030380106856742879014306200629083080552834674067/8129279490306149257242064132209950465990758789903472906716839936000000000000000)*n^23
%F A186175 + (80412737459875442438683116885876402795167547337466855388315445215859224944671/7727186096161974132690306121369458292404119107822225859717942476800000000000000)*n^22
%F A186175 + (1734677346186838180701772311707581222688214507141839590591434379086449230150843/18147179468259181675257537103216152050343006995643106185701228544000000000000000)*n^21
%F A186175 + (15613513595527478495562105742781003415900368480350353950971822442632919542996253/19261479961924219146545280609553985948171086372568560074296918016000000000000000)*n^20
%F A186175 + (3851295037244433076559382049306295935521765247943615404273761497686430913403/608174038139756216934901980030753242656407640193506996125696000000000000000)*n^19
%F A186175 + (1248332834159846499178283087535768854429210345654345356920039279433893728834953/27457931573791215868283167172499563066598552347995741788045312000000000000000)*n^18
%F A186175 + (66530283561075804307764662085931653107153334658305273611539862909313634503137953/222409245747708848533093654097246460839448274018765508483167027200000000000000)*n^17
%F A186175 + (243543913421977351315080538526951803805523324705483263739053329696279718125398251/135441527859181670581050622687425729357356320716555918627569664000000000000000)*n^16
%F A186175 + (360575016675470670217771488526138504251032819110675958867903154027738710550161/36645435026834867581453090553957177856427575951449112182784000000000000000)*n^15
%F A186175 + (15129591865697649844671536184826973429703424308626994893904682472475961112401499/309959304601978254959790724268887796035616579922673740546048000000000000000)*n^14
%F A186175 + (7524175080211648096405145864657607894725120817515555847814336181721480494149381/34439922733553139439976747140987532892846286658074860060672000000000000000)*n^13
%F A186175 + (5942762918344760659459337959632200097643470466620924337907398203629996707101419/6773184804265450756528760271060881468926436376088055811932160000000000000)*n^12
%F A186175 + (210785779932233678733122789315807742447693542136015032874568209280357413731/67103756878273864196409212481779359880780260522390978560000000000000)*n^11
%F A186175 + (75914871070809240746235724183516282036423935108451908897600806145916468306940206043/7631488426982638897605048546576608919403351832362914317800046592000000000000)*n^10
%F A186175 + (171258057108766609560163782224706210473152712219295033272952955283418686380398251/6204462135758243006182966298029763349108416123872288063252070400000000000)*n^9
%F A186175 + (422832144211051251862981353893357521977617294397809164848982147900176332404279/6375512470328019129160441559378954819885841129793579212865536000000000)*n^8
%F A186175 + (4083871966535212116585099579164103974914883024086651151131446789381574423051/30043337533787788555071525205406781145295382308055060774912000000000)*n^7
%F A186175 + (80989786688184603723123875077303914301981781664028438143150398657709186289/347439957873736330228718318701983183312939795399276213043200000000)*n^6
%F A186175 + (1361904177425071425120950053652899478573449474903883027003193336936121/4177969671401350772351110133501481280819381859058155520000000)*n^5
%F A186175 + (7685598912051770309215547476853946717707567690773419880432963550153/21439398147284320813163705347072203309166391757604454400000)*n^4
%F A186175 + (72873727609737524904444104239453351738024698064816017186401/248960261520638093925818086726071870309410457600000)*n^3
%F A186175 + (1829432107280725150019288653144625621692751793813113/11438477081703868271270325174185247025920000)*n^2
%F A186175 + (9251263324309885737154966238908069/196555536563000228097422400)*n
%F A186175 + 1061678
%e A186175 Some solutions for 4X6
%e A186175 ..0..0..0..0..0..0....0..0..0..0..0..3....0..0..0..0..0..4....0..0..0..0..1..2
%e A186175 ..0..0..0..0..0..3....0..0..0..0..1..3....0..0..0..0..2..5....0..0..0..0..1..4
%e A186175 ..0..0..0..0..5..4....0..0..0..0..5..0....0..0..0..0..3..4....0..0..0..0..1..5
%e A186175 ..0..0..0..3..4..3....0..0..0..3..3..2....0..0..0..3..2..0....0..0..0..0..2..4
%K A186175 nonn
%O A186175 1,1
%A A186175 _R. H. Hardin_ Feb 13 2011