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%I #4 Nov 17 2012 07:00:26
%S 6,17,77,261,800,2361,6647,17675,44508,106958,246970,550538,1188820,
%T 2493637,5093382,10153065,19790653,37786838,70775454,130209424,
%U 235560181,419452123,735792808,1272482264,2171035995,3656523015,6082717651
%N Number of nX3 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 nX3 array
%C Column 3 of A219299
%H R. H. Hardin, <a href="/A219294/b219294.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/20922789888000)*n^16 - (1/871782912000)*n^15 - (1/149448499200)*n^14 + (19/6227020800)*n^13 - (10039/114960384000)*n^12 + (5419/4790016000)*n^11 + (186413/7315660800)*n^10 - (332027/304819200)*n^9 + (51942799/2985984000)*n^8 - (56169313/870912000)*n^7 - (9779259841/5748019200)*n^6 + (6929296879/239500800)*n^5 - (9044060349853/48432384000)*n^4 + (7540958656897/18162144000)*n^3 + (6878088769/5765760)*n^2 - (1129882643/144144)*n + 11170 for n>7
%e Some solutions for n=3
%e ..1..1..1....0..0..2....0..0..0....0..0..1....1..1..2....0..0..0....1..1..1
%e ..1..1..1....0..1..1....0..0..2....0..1..0....1..1..2....0..0..0....1..1..1
%e ..2..2..2....1..1..1....1..2..2....1..0..0....1..2..2....1..1..1....1..2..2
%K nonn
%O 1,1
%A _R. H. Hardin_ Nov 17 2012
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