A note on Pell-Padovan numbers and their connection with Fibonacci numbers - Goy, T.P.; Sharyn, S.V. (Carpathian Mathematical Publications, 2020)
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.