- Turkish Journal of Mathematics
- Vol: 42 Issue: 3
- A new formula for hyper-Fibonacci numbers, and the number of occurrences
A new formula for hyper-Fibonacci numbers, and the number of occurrences
Authors : Takao Komatsu, Laszlo Szalay
Pages : 993-1004
View : 6 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :In this paper, we develop a new formula for hyper-Fibonacci numbers $F_n^{[k]}$, wherein the coefficients (related to Stirling numbers of the first kind) of the polynomial ingredient $p_k(n)$ are determined. As an application we investigate the number of occurrences of positive integers among $F_n^{[k]}$ and determine all the solutions in nonnegative integers $x$ and $y$ to the Diophantine equation $F_x^{[k]}=F_y^{[\ell]}$, where $0\le kKeywords : Hyper-Fibonacci numbers, Stirling numbers of the first kind, Diophantine equation, number of occurrences