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Determinantal Formulas and Recurrent Relations for Bi-Periodic Fibonacci and Lucas Polynomials

In the paper, the authors find closed formulas and recurrent relations for bi-periodic Fibonacci polynomials and for bi-periodic Lucas polynomials in terms of the Hessenberg determinants. Consequently, the authors derive closed formulas and recurrent relations for the Fibonacci, Lucas, bi-periodic Fibonacci, and bi-periodic Lucas numbers in terms of the Hessenberg determinants.