Some equalities and binomial sums about the generalized Fibonacci number u(n)

TÜRKER ULUTAŞ Y., Toy D.

NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, cilt.28, sa.2, ss.252-260, 2022 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 28 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.7546/nntdm.2022.28.2.252
  • Dergi Adı: NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.252-260
  • Anahtar Kelimeler: Generalized Fibonacci numbers, Sums of generalized Fibonacci numbers, Binomial sums, SEQUENCES, PRODUCTS, POWERS, TERMS
  • Kocaeli Üniversitesi Adresli: Evet

Özet

In this study, we take the generalized Fibonacci sequence {u(n)} as u(0) = 0; u(1) = 1 and u(n) = ru(n-1) + u(n-2) for n > 1, where r is a non-zero integer. Based on Halton's paper in [4], we derive three interrelated functions involving the terms of generalized Fibonacci sequence {u(n)}. Using these three functions we introduce a simple approach to obtain a lot of identities, binomial sums and alternate binomial sums involving the terms of generalized Fibonacci sequence {u(n)}.