Journal of Integer Sequences, Vol. 26 (2023), Article 23.4.1

Partially Palindromic Compositions

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


We generalize recent work of Andrews, Just, and Simay on modular palindromic compositions and anti-palindromic compositions by viewing all compositions partially (modular) palindromic or anti-palindromic. More precisely, we enumerate compositions by the extent to which they are (modular) palindromic or anti-palindromic. We obtain various closed formulas from generating functions and provide bijective proofs for many of them. We recover some known results of Andrews, Just, and Simay and discover new connections with numerous sequences in the On-Line Encyclopedia of Integer Sequences (OEIS).

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(Concerned with sequences A000073 A000332 A000579 A000581 A001590 A001752 A001769 A001780 A001786 A001870 A002620 A002624 A006367 A008346 A008805 A025192 A028495 A036799 A052534 A052547 A060098 A060099 A060100 A060101 A062200 A078008 A081038 A094967 A096338 A105422 A105423 A113435 A158454 A161680 A208354 A212804 A299336 A324969.)

Received March 11 2023; revised versions received April 4 2023; April 5 2023. Published in Journal of Integer Sequences, April 7 2023.

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