Some Properties of Generalized Fibonacci Numbers: Identities, Recurrence Properties and Closed Forms of the Sum Formulas ∑nk=0 xkWmk+j
Archives of Current Research International · pp. 11–38 · Published 15 Jun 2021
10.9734/acri/2021/v21i330235Abstract
In this paper, closed forms of the summation formulas ∑nk=0 xkWmk+j for generalized Fibonacci numbers are presented. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers. We present the proofs to indicate how these formulas, in general, were discovered. Of course, all the listed formulas may be proved by induction, but that method of proof gives no clue about their discovery. Moreover, we give some identities and recurrence properties of generalized Fibonacci sequence.
Cited by 5
Yüksel Soykan · Earthline Journal of Mathematical Sciences · 2022
Yüksel Soykan · Earthline Journal of Mathematical Sciences · 2021
Yüksel Soykan · Earthline Journal of Mathematical Sciences · 2022
Yüksel Soykan · Earthline Journal of Mathematical Sciences · 2021
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