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Number of (4+1)X(n+1) 0..2 arrays x(i,j) with row sums sum{x(i,j), j=1..n+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..4+1} nondecreasing.
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%I #6 Dec 08 2013 13:37:40

%S 1588,100400,5346837,241678714,9480398444,328735086329,10228591337373,

%T 289091492409655

%N Number of (4+1)X(n+1) 0..2 arrays x(i,j) with row sums sum{x(i,j), j=1..n+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..4+1} nondecreasing.

%C Row 4 of A233374.

%e Some solutions for n=2

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 08 2013