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A COMPLETE SOLUTION OF THE PARTITION OF A NUMBER INTO ARITHMETIC PROGRESSIONS
Keywords:
partition, arithmetic progression, arithmetic generated by a sequenceDOI:
https://doi.org/10.17654/0972555522006Abstract
We solve the enumeration of the set AP(n) of partitions of a positive integer n in which the nondecreasing sequence of parts forms an arithmetic progression. In particular, we establish a formula for the number of nondecreasing arithmetic progressions of positive integers with sum n. We also present an explicit method to calculate all the partitions of AP(n).
Received: November 16, 2021
Accepted: December 31, 2021
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