Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5

A Catalan Transform and Related Transformations on Integer Sequences

Paul Barry
School of Science
Waterford Institute of Technology

Abstract: 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.

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(Concerned with sequences A000007 A000027 A000035 A000045 A000079 A000108 A000129 A000217 A000225 A000245 A000344 A000957 A000984 A001006 A001045 A001333 A001477 A001791 A002057 A002426 A005408 A007179 A009545 A010892 A011782 A014300 A026641 A026674 A026726 A038503 A039599 A040000 A045891 A059841 A068875 A072547 A078008 A081696 A085478 and A087447 .)

Received December 21 2004; revised version received September 20 2005. Published in Journal of Integer Sequences September 20 2005.

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