Abstract
Let H n ( t 1, t 2, …, t m ; r) denote the number of m × n arrays of non-negative integers with row sums t 1, … t m and column sum not exceeding r. Expressions are obtained for m = 2, 3, r ⩾ t 1⩾ t 2⩾ t 3. Also, the known 3 × 3 and 4 × 4 symmetric arrays are enumerated in a particularly simple manner.
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