Table of Contents
ISRN Discrete Mathematics
Volume 2014, Article ID 374902, 7 pages
http://dx.doi.org/10.1155/2014/374902
Research Article

-Step Sum and -Step Gap Fibonacci Sequence

1Department of Computer Science and Biomedical Informatics, University of Thessaly, 2-4 Papasiopoulou street, 35100 Lamia, Greece
2Department of Electronic Engineering, Technological Educational Institute of Central Greece, 3rd km Old National Road Lamia-Athens, 35100 Lamia, Greece

Received 24 November 2013; Accepted 25 February 2014; Published 9 April 2014

Academic Editors: H. Deng, E. Gyori, and B. Zhou

Copyright © 2014 Maria Adam and Nicholas Assimakis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For two given integers , , we introduce the -step sumand -step gap Fibonacci sequence by presenting a recurrence formula that generates the th term as the sum of successive previous terms starting the sum at the th previous term. Known sequences, like Fibonacci, tribonacci, tetranacci, and Padovan sequences, are derived for specific values of , . Two limiting properties concerning the terms of the sequence are presented. The limits are related to the spectral radius of the associated -matrix.