Geodesic
A Catalan transform and related transformations on integer sequences
Journal of integer sequences, Tome 8 (2005) no. 4
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.
Classification : 11B83, 05A15, 11B37, 11B65
Keywords: integer transforms, Catalan numbers, Fibonacci numbers, jacobsthal numbers 
@article{JIS_2005__8_4_a2,
     author = {Barry,  Paul},
     title = {A {Catalan} transform and related transformations on integer sequences},
     journal = {Journal of integer sequences},
     year = {2005},
     volume = {8},
     number = {4},
     zbl = {1122.11007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2005__8_4_a2/}
}
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Barry,  Paul. A Catalan transform and related transformations on integer sequences. Journal of integer sequences, Tome 8 (2005) no. 4. http://geodesic.mathdoc.fr/item/JIS_2005__8_4_a2/