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

Takao Komatsu | Zendy; László Szalay | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

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

Author(s) -

Takao Komatsu,

László Szalay

Publication year - 2018

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1607-13

Subject(s) - fibonacci number , mathematics , diophantine equation , combinatorics , lucas number , pisano period , polynomial , discrete mathematics , fibonacci polynomials , mathematical analysis , orthogonal polynomials , difference polynomials

In this paper, we develop a new formula for hyper-Fibonacci numbers F [k] n , wherein the coefficients (related to Stirling numbers of the first kind) of the polynomial ingredient pk(n) are determined. As an application we investigate the number of occurrences of positive integers among F [k] n and determine all the solutions in nonnegative integers x and y to the Diophantine equation F [k] x = F [l] y , where 0 ≤ k < l ≤ 70. Moreover, we prove that if l is fixed, then F [k] x = F [l] y has finitely many effectively computable solutions in the nonnegative integers x , y , and k ≤ l .

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research