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Number of (n+1)X(n+1) 0..2 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 #6 Mar 31 2012 12:36:58

%S 32,480,6249,72777,808455,9149941,108633030,1362582726,17889577522,

%T 242706969233,3365618287527,47365931280277,673677478328651,

%U 9659756420132067,139434264644779578,2024155694575590620

%N Number of (n+1)X(n+1) 0..2 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 A203728

%H R. H. Hardin, <a href="/A203720/b203720.txt">Table of n, a(n) for n = 1..22</a>

%e Some solutions for n=4

%e ..0..1..1..1..0....0..1..0..2..2....1..0..1..0..1....1..2..1..1..1

%e ..2..1..1..1..2....1..1..2..2..2....1..2..1..2..1....2..1..2..2..2

%e ..1..2..2..2..2....2..2..2..2..2....2..1..2..1..2....1..2..2..2..2

%e ..1..2..2..2..2....2..2..2..2..2....1..2..1..2..2....1..2..2..2..2

%e ..2..2..2..2..2....2..2..2..2..2....2..1..2..2..2....1..2..2..2..2

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 05 2012