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%I #5 Mar 31 2012 12:36:58
%S 205,1940,1940,16842,72423,16842,131432,2634939,2634939,131432,940270,
%T 77658673,499486878,77658673,940270,6287755,1905833494,74956749750,
%U 74956749750,1905833494,6287755,39889619,40229386532,9042090593477
%N T(n,k)=Number of (n+1)X(k+1) 0..4 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 .......205...........1940...............16842.................131432
%C ......1940..........72423.............2634939...............77658673
%C .....16842........2634939...........499486878............74956749750
%C ....131432.......77658673.........74956749750.........58500223468696
%C ....940270.....1905833494.......9042090593477......36337203300044690
%C ...6287755....40229386532.....909510089895106...18604524788467098072
%C ..39889619...749063366121...78614554935810312.8110443447372955603425
%C .242721211.12535141537226.5968834286653520880
%H R. H. Hardin, <a href="/A203896/b203896.txt">Table of n, a(n) for n = 1..60</a>
%e Some solutions for n=4 k=3
%e ..3..4..3..3....2..1..2..3....3..1..0..4....3..3..2..2....0..3..4..0
%e ..4..3..4..4....2..3..3..4....1..3..4..3....3..3..4..4....3..1..0..4
%e ..3..4..4..4....1..4..4..3....3..4..3..1....2..4..4..4....1..3..4..4
%e ..4..4..2..4....1..4..4..3....4..3..4..3....2..4..4..4....2..3..2..2
%e ..4..4..2..4....3..3..1..4....4..4..3..0....2..4..4..4....2..3..4..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jan 07 2012