The sequence obtained to solve this problem—the celebrated Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, ...—appears in a large number of natural phenomena (see [2], [6]) and has natural applications in computer science (see [1]). Here we reformulate the rabbit problem to recover two generalizations of the Fibonacci sequence presented elsewhere (see [7], [8]). Then, using a fixed-point technique...

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...

We shall refer to A and B as the large and the small Golden Ratios, respectively, and shall in general simply refer to these and their powers collectively as Golden Numbers. Likewise, the ratio between the neighboring Fibonacci Numbers un+i/un will be called the large Fibonacci Ratio. Here, "large" means that the suffices n + 1 > n, without inference to the values of the u s or their ratio. Its...

1. Robert P. Backstrom. "On the Determination of the Zeros of the Fibonacci Sequence." The Fibonacci Quarterly 4, No. 4 (1966):313-322. 2. R. D. Carmichael. "On the Numerical Factors of the Arithmetic Forms a + 3." Annals of Mathematics9 2nd Ser. 15 (1913):30-70. 3. John H. Halton. "On the Divisibility Properties of Fibonacci Numbers." The Fibonacci Quarterly 4, No. 3 (1966):217-240. 4. D.H. Le...