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

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DOI:

https://doi.org/10.15330/cmp.12.2.280-288

Keywords:

Pell-Padovan sequence, Fibonacci sequence, Toeplitz-Hessenberg matrix, Trudi's formula

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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Published

2020-08-14

How to Cite

(1)
Goy, T.; Sharyn, S. A Note on Pell-Padovan Numbers and Their Connection With Fibonacci Numbers: Array. Carpathian Math. Publ. 2020, 12, 280-288.

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Section

Scientific articles

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