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Number of (n+1)X(n+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) nondecreasing in column and row directions, respectively
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%I #5 Mar 31 2012 12:36:58

%S 205,21635,2935262,443416660,66135356129,9455280188061,

%T 1324162075797758,188660753741911771,28090704419759326277

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

%C Diagonal of A203870

%e Some solutions for n=4

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

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

%e ..3..4..4..4..4....1..0..4..4..4....3..4..4..4..4....4..4..4..4..4

%e ..3..4..4..4..4....3..4..4..4..4....3..4..4..4..4....4..4..4..4..4

%e ..3..4..4..4..4....3..4..4..4..4....3..4..4..4..4....4..4..4..4..4

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 07 2012