A233299 Number of (n+1)X(3+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..3+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..n+1} nondecreasing.
22, 105, 567, 3556, 21856, 135636, 836259, 5134856, 31326263, 190404404, 1153108628, 6966626079, 42004555617, 252889763684
Offset: 1
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Examples
Some solutions for n=5 ..1..0..0..0....0..0..0..1....0..1..1..0....0..0..1..0....0..1..1..0 ..1..0..0..1....1..0..0..0....0..1..0..1....0..0..0..1....0..1..1..0 ..1..1..0..0....0..0..0..1....1..0..0..1....0..0..1..0....1..1..0..0 ..1..1..0..0....1..1..0..0....0..1..1..0....0..0..0..1....0..0..1..1 ..1..0..1..1....0..0..1..1....0..1..0..1....0..0..0..1....1..0..0..1 ..0..1..1..1....0..1..1..1....0..0..1..1....0..1..1..1....0..1..1..1
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