Formulas For Sums Of Generalized Order-k Fibonacci Type Sequences By Matrix Methods

In this paper, we give formulas for the sums of generalized order-k Fibonacci, Pell and similar other sequences which we obtain using matrix methods. As applications, we give explicit formulas for the Tribonacci and Tetranacci numbers. 1. Introduction The well-known Fibonacci sequence fFng is de…ned for n > 2 by Fn+1 = Fn + Fn 1 where F1 = F2 = 1: The well-known Pell sequence fPng is de…ned for n > 2 by Pn+1 = 2Pn + Pn 1 where P1 = 1; P2 = 2: Also, in [2], the author de…ned k sequences of generalized order-k Fibonacci numbers for n > 0 and 1 i k by