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%I #5 Mar 31 2012 12:36:58
%S 728,13006,13006,203994,1464079,203994,2788842,147040347,147040347,
%T 2788842,34183816,11575205434,111118765078,11575205434,34183816,
%U 384541867,746879546466,63988637491851,63988637491851,746879546466
%N T(n,k)=Number of (n+1)X(k+1) 0..6 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) such that rows of b(i,j) and columns of c(i,j) are lexicographically nondecreasing
%C Table starts
%C .........728............13006...............203994...............2788842
%C .......13006..........1464079............147040347...........11575205434
%C ......203994........147040347.........111118765078........63988637491851
%C .....2788842......11575205434.......63988637491851....270356138202215532
%C ....34183816.....746879546466....29334499587197078.898462061528909496153
%C ...384541867...40994270815269.11182918411649538015
%C ..4038515481.1965119386833492
%C .40101448387
%H R. H. Hardin, <a href="/A203913/b203913.txt">Table of n, a(n) for n = 1..40</a>
%e Some solutions for n=4 k=3
%e ..0..5..4..0....6..3..4..5....2..3..6..5....5..0..6..4....1..1..2..2
%e ..5..1..2..6....3..6..5..4....5..4..4..5....0..5..2..4....3..3..6..6
%e ..4..4..5..6....6..4..5..6....5..6..5..4....6..1..0..3....2..4..6..6
%e ..5..3..6..5....4..6..6..5....6..6..4..5....1..6..3..5....6..1..4..4
%e ..2..6..4..3....5..6..4..5....6..6..6..6....4..6..2..0....1..6..3..3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jan 07 2012
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