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%I #4 Nov 28 2012 13:06:22
%S 10,10,71,255,958,3227,10448,33171,104257,321192,959643,2767836,
%T 7715074,20859416,54913599,141165961,355043898,874744299,2113163842,
%U 5009479264,11662623744,26685113308,60050975462,132996270802,290066663758
%N Number of nX3 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 nX3 array
%C Column 3 of A219802
%H R. H. Hardin, <a href="/A219797/b219797.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/8841761993739701954543616000000)*n^29 - (1/60977668922342772100300800000)*n^28 + (1/764131189503042256896000000)*n^27 - (1/254710396501014085632000000)*n^26 - (89/10636258315426961817600000)*n^25 + (13033/14890761641597746544640000)*n^24 - (329653/8361122846886435225600000)*n^23 + (15731/561814578644543078400000)*n^22 + (1147/10176845001523200000)*n^21 - (428870437/58856765381809274880000)*n^20 + (96610883627/462446013714215731200000)*n^19 + (183570887/770926910216601600000)*n^18 - (12249530314366273/46512333274098224332800000)*n^17 + (232584426225439/21888156834869752627200)*n^16 - (24849998333157089/130286647826605670400000)*n^15 - (798271886098853/130286647826605670400000)*n^14 + (92782617073513847/1106330176349798400000)*n^13 - (1566383433261946709/774431123444858880000)*n^12 + (4471826683827896766467/210680466991703654400000)*n^11 - (9718227906795689456303/1158742568454370099200000)*n^10 - (204727186187491063219117/79863209605251072000000)*n^9 + (25933420961680284963641/887368995613900800000)*n^8 - (208927642534743574258367/2715547976773632000000)*n^7 - (247616287429857603924539/230163966692352000000)*n^6 + (22697987799868903204829897/2402505640562227200000)*n^5 - (6387246119388937181778481/2042129794477893120000)*n^4 - (6005949290268904522537/20091792547008000)*n^3 + (5220071206553058221/3439304668800)*n^2 - (391261681814226941/155272637520)*n + 338953 for n>16
%e Some solutions for n=3
%e ..3..0..0....2..1..1....0..0..0....1..0..0....3..0..0....2..2..2....1..0..0
%e ..3..0..0....2..0..0....0..0..0....1..0..0....3..0..0....2..2..2....1..0..0
%e ..3..0..0....2..0..0....0..0..0....1..1..1....3..2..2....2..2..2....2..2..3
%K nonn
%O 1,1
%A _R. H. Hardin_ Nov 28 2012
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