A new formula for hyper-Fibonacci numbers, and the number of occurrences

Authors

TAKAO KOMATSU
LASZLO SZALAY

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 k

DOI

10.3906/mat-1607-13

Keywords

Hyper-Fibonacci numbers, Stirling numbers of the first kind, Diophantine equation, number of occurrences

First Page

993

Last Page

1004

Recommended Citation

KOMATSU, TAKAO and SZALAY, LASZLO (2018) "A new formula for hyper-Fibonacci numbers, and the number of occurrences," Turkish Journal of Mathematics: Vol. 42: No. 3, Article 21. https://doi.org/10.3906/mat-1607-13
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/21