%I #4 Nov 13 2012 08:47:22
%S 10,53,644,5853,43013,276278,1613256,8712423,43862661,207505133,
%T 928829599,3955817599,16102004166,62882186263,236393038533,
%U 857975289846,3014067656477,10271326913737,34019623251324,109697050897692
%N Number of nX4 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 nX4 array
%C Column 4 of A219173
%H R. H. Hardin, <a href="/A219169/b219169.txt">Table of n, a(n) for n = 1..174</a>
%F Empirical: a(n) = (1/239465964362192759854596625142233314786294104064000000000)*n^48 - (1/296956801044385862914926370464079011391733760000000000)*n^47 + (106397/76425307775167902081254242066670206846689607680000000000)*n^46 - (1247461/3322839468485560960054532263768269862899548160000000000)*n^45 + (8652559/120830526126747671274710264137027995014529024000000000)*n^44 - (127932017/13133752839863877312468506971416086414622720000000000)*n^43 + (525926287/610872225109947781975279394019352856494080000000000)*n^42 - (22054773121/1003575798394914213245101861603222549954560000000000)*n^41 - (57482647423/7615209310313712187225705182897081679872000000000)*n^40 + (29866983471757/19038023275784280468064262957242704199680000000000)*n^39 - (51373262754021893/289963739123483656359748005041081187041280000000000)*n^38 + (2909441984180881/224430138640467226284634678824366243840000000000)*n^37 - (259371518756160047/536206060968035210907073124542539890688000000000)*n^36 - (3943285313579327671/191502164631441146752526115908049960960000000000)*n^35 + (1245608941431504423131/243730027712743277685033238428427223040000000000)*n^34 - (144600879256254434647/311675227254147413919479844537630720000000000)*n^33 + (105484454036954131407209/4062167128545721294750553973807120384000000000)*n^32 - (30359389674391922912439079/40621671285457212947505539738071203840000000000)*n^31 - (125538265194490804399594259/6224288342126508435504881088898007040000000000)*n^30 + (28538329249282628312273140409/7113472391001723926291292673026293760000000000)*n^29 - (6154354400432692972060914804547/22664994790639975544459153206469984256000000000)*n^28 + (629379764631642635266153142376139/56662486976599938861147883016174960640000000000)*n^27 - (43130622558154250339383435262079077/200498030840276706739446355288003706880000000000)*n^26 - (698339990020624072123683356678201501/100249015420138353369723177644001853440000000000)*n^25 + (39698725040344819356007347670347477697/47390443653156312502050956704437239808000000000)*n^24 - (30431239409785420027366493798117868023/735876454241557647547375104106168320000000000)*n^23 + (4388886419189784464797343335151127984001/3434090119793935688554417152495452160000000000)*n^22 - (22678259794412994923784749791818974423/1097854897632332381251412133150720000000000)*n^21 - (91082662218915435712432640577749213593141/324745478719643918374167708985982976000000000)*n^20 + (32051237320554607410136669218185197430734673/982782369809448700342875961404948480000000000)*n^19 - (418516484073091922482512332979184127492743520617/335128788105022006816920702839087431680000000000)*n^18 + (21021353557907639318317542715335008522337288413/704052075850886568943110720250183680000000000)*n^17 - (216883959511615332977906032342571210351289957947/523638731414096885651438598186074112000000000)*n^16 - (3305404619022071041040567228371284040436597556763/5236387314140968856514385981860741120000000000)*n^15 + (386520344437603414043765725542558753884103480641/1808300894117575362691663984066560000000000)*n^14 - (20329077100678656877495126406695030185386677183243/3051507758823408424542182973112320000000000)*n^13 + (476745152916382794559675744526380986016091036518914611/3718363921051617278918801358836465664000000000)*n^12 - (4638649532511195463938063242935547022593897509539259/2749455723936422122832594911887360000000000)*n^11 + (13920981151677298636892076278507597936846302528092581029/1032878866958782577477444821899018240000000000)*n^10 - (112723679833211318702444758596269964860664403087301081/28691079637743960485484578386083840000000000)*n^9 - (187401379566671452334364753408646849922401463739153398579/107830640971854384824612873767698432000000000)*n^8 + (160345309313698848462003658637096234500240545301575970313/5391532048592719241230643688384921600000000)*n^7 - (2306581615400479828552601689894385714776913179080487823383/7727862602982897579097255953351720960000000)*n^6 + (2177114622261374989878783658638781781049174825949938859/1082333697896764366820343971057664000000)*n^5 - (203353933955876815335484954743885696642791297367409229/22900025750954267717897970383308800000)*n^4 + (387262706201156182475003162035880179692738908473751/18174623611868466442776166970880000)*n^3 + (18734941988731977175843628396996475237475457/53873355795581812304518704000)*n^2 - (350929695958376612233355781376366331/2406090453607140300)*n + 275373669709428613 for n>27
%e Some solutions for n=3
%e ..0..0..1..2....0..0..0..0....0..0..0..0....0..0..1..0....0..0..0..1
%e ..0..0..0..1....0..0..0..0....0..0..0..1....0..1..0..0....0..0..1..1
%e ..2..0..0..0....2..2..2..2....0..1..1..1....2..1..2..0....0..1..2..2
%K nonn
%O 1,1
%A _R. H. Hardin_ Nov 13 2012
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