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Abstract.An array A = (a,;) of all the positive integers is an interspersion if the terms of any two rows, from some point on, alternate in size, and a dispersion if, for a suitable sequence (s"), the recurrence a, = sa,_, holds for each entry aj of each row of A , for j > 2 . An array is proved here to be an interspersion if and only if it is a dispersion. Such arrays whose rows satisfy certain recurrences are considered.