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.
Full version: pdf,
(Concerned with sequences
Received July 30 2010;
revised version received December 6 2010.
Published in Journal of Integer Sequences, December 8 2010.
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