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.
Full version: pdf,
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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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