Journal of Integer Sequences, Vol. 13 (2010), Article 10.9.7

A Generalization of the Binomial Interpolated Operator and its Action on Linear Recurrent Sequences

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


In this paper we study the action of a generalization of the Binomial interpolated operator on the set of linear recurrent sequences. We find how the zeros of characteristic polynomials are changed and we prove that a subset of these operators form a group, with respect to a well-defined composition law. Furthermore, we study a vast class of linear recurrent sequences fixed by these operators and many other interesting properties. Finally, we apply all the results to integer sequences, finding many relations and formulas involving Catalan numbers, Fibonacci numbers, Lucas numbers and triangular numbers.

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(Concerned with sequences A000032 A000045 A000108 A000110 A000217 A000332 A000587 A001333 A001653 A007052 A010892.)

Received July 30 2010; revised version received December 6 2010. Published in Journal of Integer Sequences, December 8 2010.

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