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In this study, we introduce a new generalization of Edouard and Edouard–Lucas numbers, the sequence of bi-periodic Edouard and bi-periodic Edouard–Lucas numbers with arbitrary initial conditions. We establish some properties and recurrences of these new sequences. In addition, the generating functions and Binet formulas are provided.

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On the Bi-periodic Edouard and the Bi-periodic Edouard–Lucas Numbers

  • 会议论文

  • 发表日期：

    2025年

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  • Eudes Antonio Costa,
  • Elen Viviani Pereira Spreafico,
  • Paula Maria Machado Cruz Catarino

摘要

In this study, we introduce a new generalization of Edouard and Edouard–Lucas numbers, the sequence of bi-periodic Edouard and bi-periodic Edouard–Lucas numbers with arbitrary initial conditions. We establish some properties and recurrences of these new sequences. In addition, the generating functions and Binet formulas are provided.