Journal of Integer Sequences, Vol. 27 (2024), Article 24.6.5

Even and Odd Compositions with Restricted Parts


Jia Huang
Department of Mathematics and Statistics
University of Nebraska at Kearney
Kearney, NE 68849
USA

Abstract:

A result of Legendre asserts that the difference between the numbers of (length) even and odd partitions of n into distinct parts is 0, 1, or –1; this also follows from Euler's pentagonal number theorem. We establish an analogous result for compositions and obtain some generalizations that are related to various entries in the On-Line Encyclopedia of Integer Sequences.


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(Concerned with sequences A000009 A003269 A010892 A014021 A014027 A014033 A050935 A081360 A099530 A122918 A281862 A339435.)


Received May 14 2024; revised version received July 20 2024. Published in Journal of Integer Sequences, July 20 2024.


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