Cassini determinant involving the $(a;b)$-hyper-Fibonacci numbers

Abstract

In the present paper, we establish some combinatorial properties of the $(a, b)$-hyper-Fibonacci numbers in order to extend the Cassini determinant.

Mathematics

Authors Imprint References Funding Related Articles Downloads

Lyes Ait-Amrane Ecole nationale Sup´ erieure d’Informatique (ESI), BP 68M Oued Smar, 16270, El Harrach, Algiers, Algeria.
Djilali Behloul Facult ´e d’Informatique,USTHB, BP 32, El Alia, 16111, Bab Ezzouar, Algiers, Algeria. https://orcid.org/0000-0003-4631-5529

N. G. Voll, The Cassini identity and its relatives, Fibonacci Quart., 48(3)(2010), 197-201.

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, 1994.

E. P. Miles, Jr., Generalized Fibonacci numbers and associated matrices, Amer. Math. Monthly, 67(1960), 745752.

M. Werman and D. Zeilberger, A bijective proof of Cassini's Fibonacci identity, Discrete Math., 58(1)(1986), 109.

I. Martinjak and I. Urbiha, A new generalized Cassini determinant, Colloquium Mathematicum, 145(2016), 209218.

A. Dil and I. Mező, A symmetric algorithm for hyperharmonic and Fibonacci numbers, Appl. Math. Comput., 206(2)(2008), 942-951.

N. N. Cao and F. Z. Zhao, Some properties of hyperfibonacci and hyperlucas numbers, J. Integer Seq., 13(8)(2010), Article 10.8.8, $11 mathrm{pp}$.

Metrics Loading ...