NOTE ON A PARTITION-FUNCTION

Let T(n) denote the number of partitions of n into parts which are repeated exactly 1, 3, 4, 6, 7, 9, or 10 times with the parts repeated exactly 3, 4, 6, or 7 times being even in number minus the number of them with the parts repeated exactly 3, 4, 6, or 7 times being odd in number. In this note we prove that T(n) is non-negative and assumes all non-negative integral values infinitely often. © 1992.