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%I #4 Nov 23 2012 10:42:44
%S 10,51,415,2234,10226,43194,175054,681294,2520724,8826995,29312128,
%T 92766392,281352528,821894587,2322377790,6369721171,17006832588,
%U 44306213351,112846664535,281447430087,688297677269,1652410927948
%N Number of nX3 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 nX3 array
%C Column 3 of A219578
%H R. H. Hardin, <a href="/A219573/b219573.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/552610124608731372158976000000)*n^29 + (1/3811104307646423256268800000)*n^28 + (1/129629398219266097152000000)*n^27 - (31/604937191689908453376000000)*n^26 + (877/46533630129992957952000000)*n^25 + (239/372269041039943663616000)*n^24 + (33503/24430155818246302924800000)*n^23 + (5591879/8497445501998714060800000)*n^22 - (231247/12261826121210265600000)*n^21 + (12158051/7357095672726159360000)*n^20 + (2445075107/202320130999969382400000)*n^19 - (56854384157/21296855894733619200000)*n^18 + (137907619368839/1162808331852455608320000)*n^17 - (135165120005483/68400490108967976960000)*n^16 - (48023952636601/4071457744581427200000)*n^15 + (28424142664663183/16285830978325708800000)*n^14 - (84408492721776677/1638219684210278400000)*n^13 + (724628434108627231/851874235789344768000)*n^12 - (155602913726221679243/26335058373962956800000)*n^11 - (48964593179833669647503/579371284227185049600000)*n^10 + (76233590865481207417073/23709390351558912000000)*n^9 - (432565114735770248700887/8430005458332057600000)*n^8 + (85694644782598196110159/166229531500032000000)*n^7 - (86412687664576691056232021/26929184103005184000000)*n^6 + (464222833288478856269869001/68070993149263104000000)*n^5 + (182634752184978211634207821/2042129794477893120000)*n^4 - (5379349472699128084793279/4862213796375936000)*n^3 + (121933503571229586701/19688264481600)*n^2 - (14552066068591182739/776363187600)*n + 24775150 for n>10
%e Some solutions for n=3
%e ..0..0..0....1..0..0....1..1..1....2..0..0....1..0..0....2..1..0....1..0..0
%e ..0..0..0....0..0..0....3..1..1....2..2..0....1..1..0....1..0..0....1..1..0
%e ..1..1..0....3..0..0....3..2..1....2..2..3....2..1..2....1..0..0....3..0..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Nov 23 2012
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