Geodesic
Generalization of the Fibonacci Sequence to n Dimensions
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 332-349

Voir la notice de l'article provenant de la source Cambridge University Press

We introduce certain n X n matrices with integral elements that constitute a free semigroup with identity and generate the n-dimensional unimodular group. In terms of these matrices we define a certain sequence of n-dimensional vectors, which we show is the natural generalization to n dimensions of the Fibonacci sequence. Connections between the generalized Fibonacci sequences and certain Jacobi polynomials are found. The various basic identities concerning the Fibonacci numbers are shown to have natural extensions to n dimensions, and in some cases the proofs are rendered quite brief by the use of known theorems on matrices. 
Raney, George N. Generalization of the Fibonacci Sequence to n Dimensions. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 332-349. doi: 10.4153/CJM-1966-036-0
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