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2020•Notes on Number Theory and Discrete MathematicsOpen access

Identities on generalized Fibonacci and Lucas numbers

K. M. Nagaraja, P. Dhanya

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Abstract

In this article, the concepts of Fibonacci, Tribonacci, Lucas and Tetranacci numbers are generalized as continued sum.The generalized Fibonacci identity is proved by using induction and the binomial theorem.Further, it is proved that the generalized Fibonacci and Lucas sequences are logarithmically convex (concave) and some special identities are obtained.

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In this article, the concepts of Fibonacci, Tribonacci, Lucas and Tetranacci numbers are generalized as continued sum.The generalized Fibonacci identity is proved by using induction and the binomial theorem.Further, it is proved that the generalized Fibonacci and Lucas sequences are logarithmically convex (concave) and some special identities are obtained.

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Available abstract

In this article, the concepts of Fibonacci, Tribonacci, Lucas and Tetranacci numbers are generalized as continued sum.The generalized Fibonacci identity is proved by using induction and the binomial theorem.Further, it is proved that the generalized Fibonacci and Lucas sequences are logarithmically convex (concave) and some special identities are obtained.

Key concepts: Fibonacci number, Lucas number, Lucas sequence, Fibonacci polynomials, Mathematics, Pisano period, Combinatorics, Orthogonal polynomials

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