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%I #6 Nov 20 2012 17:10:06
%S 15,53,344,2275,11861,60738,278221,1210223,4982663,19591906,73766878,
%T 266405385,926295032,3109222072,10103620683,31853913050,97605116782,
%U 291102100195,846145644323,2399919368153,6649637316141,18018812905279
%N Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 4Xn array
%C Row 4 of A219381
%H R. H. Hardin, <a href="/A219384/b219384.txt">Table of n, a(n) for n = 1..102</a>
%F Empirical: a(n) = (1/12413915592536072670862289047373375038521486354677760000000000)*n^48 - (1/12615767878593569787461675861151803900936469872640000000000)*n^47 + (109/2641258636709802695928146605824122348621592841420800000000)*n^46 - (149/10401932249172190831475057521361540440381194240000000000)*n^45 + (985373/273422219121097587570201511990074777290019962880000000000)*n^44 - (1163/1733580001818474480268439944577159182417920000000000)*n^43 + (15411871/173417897962641176048753601685036856632147968000000000)*n^42 - (3365407229/505802202391036763475531338248024165177098240000000000)*n^41 - (170752212793/592158675969994259678670835022077071426846720000000000)*n^40 + (4540140963283/24673278165416427486611284792586544642785280000000000)*n^39 - (44184245813/1349540350154545782669803255524101193728000000000)*n^38 + (155915806367/42808553793974113288513767629893140480000000000)*n^37 - (82168196085078487/330915740483130301588365128289110332538880000000000)*n^36 + (17664152146313879/6032318185890396122704572651103573770240000000000)*n^35 + (406603192224319620001/231641018338191211111855589802377232777216000000000)*n^34 - (137013510748443392467/516134176332868117450658622554316472320000000000)*n^33 + (298492435966333310210023/13370332948813345518721823365216579092480000000000)*n^32 - (4300620354947005285913021/3899680443403892442960531814854835568640000000000)*n^31 + (24455489604418848190234867/3687624087495293683389406121696830685184000000000)*n^30 + (2066968682227094010621342701/467633489356287242458801500939815485440000000000)*n^29 - (45328310017380394562286088474987/97912777495564694352063541851950331985920000000000)*n^28 + (3216720130246483969893215555233/119991148891623399941254340504841093120000000000)*n^27 - (140192576026014788197138617874541/164981236805713404402744429494128764518400000000)*n^26 - (4633190765348202684872547320742023/801992123361106826957785421152014827520000000000)*n^25 + (1605102772723515720944647568910214328029/643426823542282277170703275027102181621760000000000)*n^24 - (120814681020899799074798787413189496041/741763465875490108727754104939017666560000000000)*n^23 + (158612826112596530631853771122674004769/26179887030899650896273674291965329408000000000)*n^22 - (10084399261409658331822687169841866418853/92720433234436263590969263117377208320000000000)*n^21 - (3355395666385571466257090354087761380406271/1536510036456372368078919217373679452160000000000)*n^20 + (1900831468152110143365206682938023257113851/7862258958475589602743007691239587840000000000)*n^19 - (4885965975470694309483510604620056126081344463/517055844504891096231820512951734894592000000000)*n^18 + (2374979297857136445529736513661313295546190241/11088820194651463460853993843940392960000000000)*n^17 - (73561520162539087269773556740821945080689749367869/36193909115342376736227435906621442621440000000000)*n^16 - (3186872875527961878865445361304302558287658108787/65568675933591262203310572294604062720000000000)*n^15 + (2832781635211470687533340746631769446873140409101/1104820180566006615879958361007980544000000000)*n^14 - (8684326768420376833999278082392535766954821585109/146472372423523604378024782709391360000000000)*n^13 + (228832573286455000231181947684304841529108516624761679/254973526014968041983003521748786216960000000000)*n^12 - (45815449009661676216776396864884733319179356438832699/4374545789472490916375060422160547840000000000)*n^11 + (305662140564014658874583462443691416438435227229858777/2478909280701078185945867572557643776000000000)*n^10 - (762722309065001353588330355580622975862119821987846173/516439433479391288738722410949509120000000000)*n^9 + (718973363076692716089675024721187765328272735123255521/158445023468847259334125039005597696000000000)*n^8 + (848161288858472673679833479892013465023555534894493/2213196886501988536748459763302400000000)*n^7 - (56317491837131215740599391035262923026943332132050051109/5454961837399692408774533614130626560000000)*n^6 + (2155022928401289408616035562092828046303221935441510941/15771148169352852202239297863983104000000)*n^5 - (1037017090357524744827112413977884523447798855998152317/1007601133041987779587510696865587200000)*n^4 + (482202514103145343561819110186201001893614609219/126652429350999766151750292480000)*n^3 + (720940876656049003682323347354238969101978739/2370427655005599741398822976000)*n^2 - (137242300008728865972259181934158332/2767004021648211345)*n + 109003811773948140 for n>50
%e Some solutions for n=3
%e ..0..1..0....0..0..0....0..0..2....1..1..1....0..0..1....0..0..2....0..0..0
%e ..0..0..0....0..0..0....0..0..1....1..0..1....1..0..0....2..0..2....0..0..0
%e ..0..0..0....0..0..1....1..0..1....1..0..0....2..0..0....2..2..2....0..0..1
%e ..0..0..0....1..0..2....1..2..1....2..0..1....2..0..2....2..2..2....1..0..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Nov 19 2012
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