A note on Pell-Padovan numbers and their connection with Fibonacci numbers

Keywords: Pell-Padovan sequence, Fibonacci sequence, Toeplitz-Hessenberg matrix, Trudi's formula
Published online: 2020-08-14

Abstract


In this paper, we find new relations involving the Pell-Padovan sequence which arise as determinants of certain families of Toeplitz-Hessenberg matrices. These determinant formulas may be rewritten as identities involving sums of products of Pell-Padovan numbers and multinomial coefficients. In particular, we establish four connection formulas between the Pell-Padovan and the Fibonacci sequences via Toeplitz-Hessenberg determinants.

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