Abstract
In this paper, we consider compositions of integers when only parts of size at most 3 are allowed in both composition and its conjugate composition. First we obtain a relation between the number of such compositions and the Fibonacci numbers. Then we provide combinatorial identities between these compositions and compositions into 1’s and 2’s, compositions into odd parts, and compositions into parts greater than 1. Further, several generalized results for these compositions are obtained.
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The author would like to thank the referees for their valuable comments and corrections which have improved the quality of this paper.
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Communicated by Sanoli Gun.
This work was supported by the National Natural Science Foundation of China(Grant No. 11461020).
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Guo, Y. Some identities for compositions into parts of size at most 3. Indian J Pure Appl Math 53, 587–592 (2022). https://doi.org/10.1007/s13226-021-00149-x
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DOI: https://doi.org/10.1007/s13226-021-00149-x