Geodesic
Fixed sequences for a generalization of the binomial interpolated operator and for some other operators
Journal of integer sequences, Tome 14 (2011) no. 8.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 11B37, 11B39
Keywords: binomial operator, Catalan numbers, Fibonacci numbers, invert operator, Motzkin numbers, recurrent sequences, revert operator (Concerned with sequences and ) 
@article{JIS_2011__14_8_a4,
     author = {Abrate, Marco and Barbero, Stefano and Cerruti, Umberto and Murru, Nadir},
     title = {Fixed sequences for a generalization of the binomial interpolated operator and for some other operators},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {14},
     number = {8},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_8_a4/}
}
TY  - JOUR
AU  - Abrate, Marco
AU  - Barbero, Stefano
AU  - Cerruti, Umberto
AU  - Murru, Nadir
TI  - Fixed sequences for a generalization of the binomial interpolated operator and for some other operators
JO  - Journal of integer sequences
PY  - 2011
VL  - 14
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JIS_2011__14_8_a4/
LA  - en
ID  - JIS_2011__14_8_a4
ER  - 
%0 Journal Article
%A Abrate, Marco
%A Barbero, Stefano
%A Cerruti, Umberto
%A Murru, Nadir
%T Fixed sequences for a generalization of the binomial interpolated operator and for some other operators
%J Journal of integer sequences
%D 2011
%V 14
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JIS_2011__14_8_a4/
%G en
%F JIS_2011__14_8_a4
Abrate, Marco; Barbero, Stefano; Cerruti, Umberto; Murru, Nadir. Fixed sequences for a generalization of the binomial interpolated operator and for some other operators. Journal of integer sequences, Tome 14 (2011) no. 8. http://geodesic.mathdoc.fr/item/JIS_2011__14_8_a4/