Takao KOMATSU, Laszlo SZALAY

8188

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

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

Keywords:

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

Turkish Journal of Mathematics-Cover

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

Arşiv

Sayıdaki Diğer Makaleler

Leonid A. KURDACHENKO, Marco TROMBETTI

Mariusz ZYNEL, Krzysztof PETELCZYC, Krzysztof PRAZMOWSKI, Malgorzata PRAZMOWSKA

Nak Eun CHO, Sushil KUMAR, Virendra KUMAR, V. RAVICHANDRAN

Connection between bi snomial coefficients and their analogs and symmetric functions

Moussa AHMIA, Abdelghafour BAZENIAR, Hacene BELBACHIR

On hypersurfaces with parallel M¨obius form and constant para-Blaschke eigenvalues

Xiuli GUO, Shujie ZHAI, Zejun HU

On reflexivity of the Bochner space $L^p$ (µ, E) for arbitrary µ

Bahaettin CENGİZ, Banu GÜNTÜRK

Pooja GUPTA, Purshottam Narain AGRAWAL

Arjun Kumar RATHIE, Luan Carlos de Sena Monteiro OZELIM, Pushpa Narayan RATHIE

Uğur GÖNÜLLÜ