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%I #5 Mar 31 2012 12:36:04
%S 102251,1252889,11258613,83378583,531218757,2985984444,15084070635,
%T 69482992431,295278398390,1168636004931,4340861873151,15229963644864,
%U 50743091539034,161283018943658,490947611660031,1436133677832325
%N Number of (n+2)X3 0..4 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order
%C Column 1 of A186096
%H R. H. Hardin, <a href="/A186088/b186088.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = (1/295232799039604140847618609643520000000)*n^34
%F + (1/36561337342365837875866081689600000)*n^33
%F + (1151/78939251080108059050165403648000000)*n^32
%F + (57793/15180625207713088278877962240000000)*n^31
%F + (8146051/12732137270985170814542807040000000)*n^30
%F + (15252793/195879034938233397146812416000000)*n^29
%F + (917629/125082397789421070974976000000)*n^28
%F + (40844936773/73173202706811326520360960000000)*n^27
%F + (10326664514897/292692810827245306081443840000000)*n^26
%F + (1699793021071/900593264083831711019827200000)*n^25
%F + (21419403120091/247663147623053720530452480000)*n^24
%F + (3257433593147959/952550567780975848194048000000)*n^23
%F + (149148353528547551/1272577438379327417745408000000)*n^22
%F + (888681424414566953/254515487675865483549081600000)*n^21
%F + (11531836957656612161/127257743837932741774540800000)*n^20
%F + (5909972330146165909/2879134475971328999424000000)*n^19
%F + (185196564663366054480883/4554487674199698126667776000000)*n^18
%F + (223744365124534317893/317054484803320440422400000)*n^17
%F + (631124705896508562289697/58734343309815111588249600000)*n^16
%F + (7215220158705833717523107/50233319936026082279424000000)*n^15
%F + (44200951728497459126549888033/26246909666573627990999040000000)*n^14
%F + (1394814879695359558279349521/80759722050995778433843200000)*n^13
%F + (32548509299450082036607825951/211076546269648057270272000000)*n^12
%F + (48337137666188129039919297713/40591643513393857167360000000)*n^11
%F + (18053107623124660173941442743743/2286662584587853953761280000000)*n^10
%F + (2266224377869928249871300899693/50814724101952310083584000000)*n^9
%F + (902210285827865272553906095027/4234560341829359173632000000)*n^8
%F + (57964514565563064206413856761/67861543939573063680000000)*n^7
%F + (2023140467628393995969236886677/710661168478306805760000000)*n^6
%F + (25417310330253175708558630751/3279974623746031411200000)*n^5
%F + (61858293620765291251250539109/3728237822324655704064000)*n^4
%F + (12364083190538430205351213/471396394434917952000)*n^3
%F + (8255316109684330210707767/294877831150846944000)*n^2
%F + (1418176238189177/80224196052)*n
%F + 2040
%e Some solutions for 4X3
%e ..0..0..1....0..0..0....0..0..0....0..0..0....0..0..0....0..0..1....0..0..0
%e ..0..0..3....0..3..3....0..0..3....0..1..4....0..1..1....0..0..1....0..0..1
%e ..1..4..2....1..2..2....0..2..3....0..3..3....2..0..2....0..1..2....2..3..3
%e ..4..4..2....1..4..4....3..1..0....1..3..2....4..0..0....0..3..0....3..3..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Feb 12 2011
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