Takao Komatsu, José L. Ramírez

Convolutions of the bi-periodic Fibonacci numbers

Let $q_n$ be the bi-periodic Fibonacci numbers, defined by $q_n=c(n)q_{n-1}+q_{n-2}$ ($n\ge 2$) with $q_0=0$ and $q_1=1$, where $c(n)=a$ if $n$ is even, $c(n)=b$ if $n$ is odd, where $a$ and $b$ are nonzero real numbers. When $c(n)=a=b=1$, $q_n=F_n$ are Fibonacci numbers. In this paper, the convolution identities of order $2$, $3$ and $4$ for the bi-periodic Fibonacci numbers $q_n$ are given with binomial (or multinomial) coefficients, by using the symmetric formulas.

Keywords:

bi-periodic Fibonacci numbers convolutions, symmetric formulas,

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Hacettepe Journal of Mathematics and Statistics-Cover

Yayın Aralığı: 6
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

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