K-Step Sum and m-Step Gap Fibonacci Sequence. (9th April 2014) - Adam, Maria; Assimakis, Nicholas
Abstract : For two given integersk, m, we introduce thek -step sumandm -step gap Fibonacci sequence by presenting a recurrence formula that generates then th term as the sum ofk successive previous terms starting the sum at them th previous term. Known sequences, like Fibonacci, tribonacci, tetranacci, and Padovan sequences, are derived for specific values ofk, 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.