Journal of Integer Sequences, Vol. 25 (2022), Article 22.5.8

Permanental Representations of Negatively Subscripted Generalized Order-k Fibonacci Numbers


Hacène Belbachir
USTHB
Faculty of Mathematics
RECITS Laboratory
P. O. Box 32
El Alia, 16111, Algiers
Algeria

Ihab-Eddine Djellas
USTHB
Faculty of Mathematics
RECITS Laboratory
P. O. Box 32
El Alia, 16111, Algiers
Algeria
Centre de Recherche sur l'Information Scientifique et Technique--CERIST
Algiers, Algeria

Fariza Krim
Oran 1 University
Faculty of Sciences
GEAN Laboratory
P. O. Box 1524
El Menaouer, 31000, Oran
Algeria
USTHB
Faculty of Mathematics
RECITS Laboratory
P. O. Box 32
El Alia, 16111, Algiers
Algeria

Abstract:

We introduce an extension to the negative indices of a family of generalized Fibonacci sequences of order-k, and for which we establish recurrence relations. We also give permanental representations of negatively subscripted generalized Fibonacci and Lucas sequences via Hessenberg matrices.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A077990 A078021 A078064 A215936 A276229.)

Received December 20 2021; revised versions received December 22 2021; June 16 2022; June 19 2022. Published in Journal of Integer Sequences, June 22 2022.

Return to Journal of Integer Sequences home page