##
**
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

Turin

Italy

**Abstract:**

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,
dvi,
ps,
latex
**

(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.

Return to
**Journal of Integer Sequences home page**