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Number of (n+1)X(n+1) 0..5 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) nondecreasing in column and row directions, respectively
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%I #5 Mar 31 2012 12:37:00

%S 406,91396,32094464,14543414270,7208336070660,3601865763979034,

%T 1772878084052954152

%N Number of (n+1)X(n+1) 0..5 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) nondecreasing in column and row directions, respectively

%C Diagonal of A203944

%e Some solutions for n=4

%e ..1..0..4..3..4....1..4..0..5..5....1..5..2..3..3....4..5..4..4..4

%e ..2..4..3..4..3....4..1..5..5..5....4..2..5..4..4....5..4..5..5..5

%e ..3..3..4..3..5....2..5..5..5..5....1..5..4..5..5....4..5..5..5..5

%e ..3..5..4..5..5....2..5..5..5..5....3..4..5..5..5....4..5..5..5..5

%e ..5..4..5..5..5....2..5..5..5..5....5..4..5..5..5....4..5..5..5..5

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 08 2012