Journal of Integer Sequences, Vol. 21 (2018), Article 18.6.6

Some Identities For Palindromic Compositions

Yu-hong Guo
School of Mathematics and Statistics
Hexi University
Zhangye, Gansu, 734000
P. R. China


This paper considers self-inverse or palindromic compositions of positive integers into parts ≤ 3. First we obtain two classes of such compositions that are enumerated by the Fibonacci numbers. Then we provide combinatorial identities between palindromic compositions and compositions into 1's and 2's, compositions into odd parts, and compositions into parts greater than 1.

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(Concerned with sequence A055389.)

Received October 11 2017; revised versions received October 14 2017; October 24 2017; May 12 2018; June 9 2018; June 11 2018. Published in Journal of Integer Sequences, August 22 2018.

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