Polymatrix and generalized polynacci numbers

Details Polymatrix and generalized polynacci numbers Polymatrix and generalized polynacci numbers

2002-10-14

arxiv.org/abs/math/0210201v1

Mathematics

Combinatorics

Scientific paper

We consider $m$-th order linear recurrences that can be thought of as generalizations of the Lucas sequence. We exploit some interplay with matrices that again can be considered generalizations of the Fibonacci matrix. We introduce the definition of reflected sequence and inverted sequence and we establish some relationship between the coefficients of the Cayley-Hamilton equation for these matrices and the introduced sequences.

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