A note on Pell-Padovan numbers and their connection with Fibonacci numbers
Copyright policy )A note on Pell-Padovan numbers and their connection with Fibonacci numbers
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.
trudi's formula, Toeplitz-Hessenberg matrix, Matrices, determinants in number theory, toeplitz-hessenberg matrix, fibonacci sequence, Special sequences and polynomials, QA1-939, pell-padovan sequence, Fibonacci and Lucas numbers and polynomials and generalizations, Fibonacci sequence, Trudi's formula, Mathematics, Pell-Padovan sequence
trudi's formula, Toeplitz-Hessenberg matrix, Matrices, determinants in number theory, toeplitz-hessenberg matrix, fibonacci sequence, Special sequences and polynomials, QA1-939, pell-padovan sequence, Fibonacci and Lucas numbers and polynomials and generalizations, Fibonacci sequence, Trudi's formula, Mathematics, Pell-Padovan sequence
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