%I #4 Jan 29 2016 07:24:34
%S 2,9,4,64,81,6,615,4096,576,9,7536,378225,216000,3969,12,112476,
%T 56791296,197555340,10941048,25281,16,1981512,12650850576,
%U 371713931400,98956027822,519718464,155236,20,40265487,3926389806144,1257212773492866
%N T(n,k)=Number of nXk 0..k arrays with every repeated value in every row greater than or equal to, and every column greater than, the previous repeated value.
%C Table starts
%C ..2......9..........64............615.............7536................112476
%C ..4.....81........4096.........378225.........56791296...........12650850576
%C ..6....576......216000......197555340.....371713931400......1257212773492866
%C ..9...3969....10941048....98956027822.2335306173137957.120138605995104637373
%C .12..25281...519718464.46876747497685
%C .16.155236.23689358848
%C .20.915849
%C .25
%H R. H. Hardin, <a href="/A268246/b268246.txt">Table of n, a(n) for n = 1..40</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4)
%F k=2: [order 15]
%F k=3: [order 40]
%e Some solutions for n=2 k=4
%e ..1..1..0..1....0..0..2..0....0..1..2..0....0..2..2..2....1..1..2..3
%e ..1..0..2..2....3..4..4..3....2..3..1..2....0..3..0..1....1..0..4..2
%Y Column 1 is A002620(n+2).
%Y Column 2 is A267961.
%Y Column 3 is A267971.
%Y Row 1 is A268104.
%Y Row 2 is A268105.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 29 2016