A Catalan transform and related transformations on integer sequences

Paul Barry

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


We introduce and study an invertible transformation on integer sequences related to the Catalan numbers. Transformation pairs are identified among classical sequences. A closely related transformation which we call the generalized Ballot transform is also studied, along with associated transformations. Results concerning the Fibonacci, Jacobsthal and Pell numbers are derived. Finally, we derive results about combined transformations.

Original languageEnglish
JournalJournal of Integer Sequences
Issue number4
Publication statusPublished - 20 Sep 2005


  • Catalan numbers
  • Fibonacci numbers
  • Integer transforms
  • Jacobsthal numbers


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