Journal of Integer Sequences, Vol. 14 (2011), Article 11.8.1

Fixed Sequences for a Generalization of the Binomial Interpolated Operator and for some Other Operators

Marco Abrate, Stefano Barbero, Umberto Cerruti, and Nadir Murru
Department of Mathematics
University of Turin
via Carlo Alberto 8/10


This paper is devoted to the study of eigen-sequences for some important operators acting on sequences. Using functional equations involving generating functions, we completely solve the problem of characterizing the fixed sequences for the Generalized Binomial operator. We give some applications to integer sequences. In particular we show how we can generate fixed sequences for Generalized Binomial and their relation with the Worpitzky transform. We illustrate this fact with some interesting examples and identities, related to Fibonacci, Catalan, Motzkin and Euler numbers. Finally we find the eigen-sequences for the mutual compositions of the operators Interpolated Invert, Generalized Binomial and Revert.

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(Concerned with sequences A000045 A000108 A000984 A001006 A001850 A101890 A115865 A155585.)

Received April 10 2011; revised version received August 2 2011. Published in Journal of Integer Sequences, September 25 2011.

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