Polymatrix and Generalized Polynacci Numbers
نویسنده
چکیده
We considerm-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. 1 Antefacts Let us define the m × m matrix Am as a matrix with the first column of all ones, as well as the first upper diagonal, while all the other elements are equal to zero, that is
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