K-Step Sum and m-Step Gap Fibonacci Sequence. (9th April 2014)

• Record Type: Journal Article
• Authors: Adam, Maria; Assimakis, Nicholas
• Other Names: Deng H. Academic Editor.; Gyori E. Academic Editor.; Zhou B. Academic Editor.
• Is Part Of: ISRN discrete mathematics. Volume 2014(2014)
• Publication Date: 2014-04-09
• Subjects: Discrete mathematics -- Periodicals; Computer science -- Mathematics; Computer science -- Mathematics; Periodicals; 511.1
• DOI: 10.1155/2014/374902
• Languages: English
• ISSNs: 2090-7788

Abstract

Abstract : For two given integers k, m, we introduce the k -step sumand m -step gap Fibonacci sequence by presenting a recurrence formula that generates the n th term as the sum of k successive previous terms starting the sum at the m th previous term. Known sequences, like Fibonacci, tribonacci, tetranacci, and Padovan sequences, are derived for specific values of k, m . Two limiting properties concerning the terms of the sequence are presented. The limits are related to the spectral radius of the associated { 0, 1 } -matrix.