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%I #4 Nov 19 2012 06:30:13
%S 6,14,84,344,1271,4116,12452,35741,97942,256627,644220,1553493,
%T 3608625,8096762,17592376,37102211,76113986,152179500,297049058,
%U 566965708,1059617705,1941564060,3491864902,6170398463,10723237448,18342891239
%N Number of nX3 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 nX3 array
%C Column 3 of A219381
%H R. H. Hardin, <a href="/A219376/b219376.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/10461394944000)*n^16 + (1/261534873600)*n^15 - (43/523069747200)*n^14 + (37/9340531200)*n^13 + (3161/57480192000)*n^12 - (3877/1437004800)*n^11 + (330221/3657830400)*n^10 - (286723/228614400)*n^9 + (588676351/73156608000)*n^8 + (6080057/52254720)*n^7 - (9539004331/2874009600)*n^6 + (28480226939/718502400)*n^5 - (57210329051177/217945728000)*n^4 + (810763395331/908107200)*n^3 - (144144166781/302702400)*n^2 - (2133172367/360360)*n + 12653 for n>6
%e Some solutions for n=3
%e ..1..1..2....0..0..1....1..1..1....1..1..1....0..0..0....2..2..2....0..0..1
%e ..1..1..1....0..0..1....0..1..0....1..1..1....0..0..0....2..2..2....0..0..0
%e ..1..1..1....2..0..0....0..0..0....2..1..2....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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