Journal of Integer Sequences, Vol. 20 (2017), Article 17.6.7

Extending a Recent Result on Hyper m-ary Partition Sequences

Timothy B. Flowers
Department of Mathematics
Indiana University of Pennsylvania
Indiana, PA 15705

Shannon R. Lockard
Department of Mathematics
Bridgewater State University
Bridgewater, MA 02324


A hyper m-ary partition of an integer n is defined to be a partition of n where each part is a power of m and each distinct power of m occurs at most m times. Let hm(n) denote the number of hyper m-ary partitions of n and consider the resulting sequence. We show that the hyper m1-ary partition sequence is a subsequence of the hyper m2-ary partition sequence, for 2 ≤ m1m2.

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(Concerned with sequences A002487 A054390 A277872 A277873.)

Received June 30 2016; revised versions received February 9 2017; June 13 2017; June 23 2017. Published in Journal of Integer Sequences, July 1 2017. Minor revision, July 30 2017.

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