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Extending a Recent Result on Hyper ***m*-ary Partition Sequences

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Timothy B. Flowers

Department of Mathematics

Indiana University of Pennsylvania

Indiana, PA 15705

USA

Shannon R. Lockard

Department of Mathematics

Bridgewater State University

Bridgewater, MA 02324

USA

**Abstract:**

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 *h*_{m}(*n*) denote the number
of hyper *m*-ary partitions
of *n* and consider the resulting sequence.
We show that the hyper *m*_{1}-ary
partition sequence is a subsequence of the
hyper *m*_{2}-ary partition sequence,
for 2 ≤ *m*_{1} ≤ *m*_{2}.

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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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