AbstractSome new identities for the Fibonomial coefficients are derived. These identities are related to the generating function of the kth powers of the Fibonacci numbers. Proofs are based on manipulation with the generating function of the sequence of “signed Fibonomial triangle”
A combinatorial argument is used to explain the integrality of Fibonomial coefficients and their gen...
The Fibonacci numbers are sequences of numbers of the form: 0,1,1,2,3,5,8,13,... Among n...
The Fibonacci numbers are sequences of numbers of the form: 0,1,1,2,3,5,8,13,... Among n...
In this paper a new method of generating identities for Fibonacci and Lu- cas numbers is presented....
In this paper, we introduce several convolution identities that combine Fibonacci and Pell numbers. ...
AbstractIn this paper following some ideas introduced by Andrews (Combinatorics and Ramanujan's “los...
The Fibonomial numbers are defined by \[ \begin{bmatrix}n \\ k \end{bmatrix} = \frac{\prod_{i=n-k+...
It is known that the generating function of the Fibonacci sequence, F(t) =\sum_{k=0}^{\infty} F_k t^...
We can define Fibonomial coefficients as an analogue to binomial coefficients as F(n,k) = FnFn-1 … F...
Based on well-known properties of Fibonacci and Lucas numbers and polynomials we give a self-contain...
We provide elementary combinatorial proofs of several Fibonacci and Lucas number identities left ope...
We provide a list of simple looking identities that are still in need of combinatorial proof
The Fibonomial numbers are defined by \[ \begin{bmatrix}n \\ k \end{bmatrix} = \frac{\prod_{i=n-k+...
Five binomial sums are extended by a free parameter $m$, that are shown, through the generating func...
In this paper, we show that sum of the row elements on the table formed by given recurrence relatio...
A combinatorial argument is used to explain the integrality of Fibonomial coefficients and their gen...
The Fibonacci numbers are sequences of numbers of the form: 0,1,1,2,3,5,8,13,... Among n...
The Fibonacci numbers are sequences of numbers of the form: 0,1,1,2,3,5,8,13,... Among n...
In this paper a new method of generating identities for Fibonacci and Lu- cas numbers is presented....
In this paper, we introduce several convolution identities that combine Fibonacci and Pell numbers. ...
AbstractIn this paper following some ideas introduced by Andrews (Combinatorics and Ramanujan's “los...
The Fibonomial numbers are defined by \[ \begin{bmatrix}n \\ k \end{bmatrix} = \frac{\prod_{i=n-k+...
It is known that the generating function of the Fibonacci sequence, F(t) =\sum_{k=0}^{\infty} F_k t^...
We can define Fibonomial coefficients as an analogue to binomial coefficients as F(n,k) = FnFn-1 … F...
Based on well-known properties of Fibonacci and Lucas numbers and polynomials we give a self-contain...
We provide elementary combinatorial proofs of several Fibonacci and Lucas number identities left ope...
We provide a list of simple looking identities that are still in need of combinatorial proof
The Fibonomial numbers are defined by \[ \begin{bmatrix}n \\ k \end{bmatrix} = \frac{\prod_{i=n-k+...
Five binomial sums are extended by a free parameter $m$, that are shown, through the generating func...
In this paper, we show that sum of the row elements on the table formed by given recurrence relatio...
A combinatorial argument is used to explain the integrality of Fibonomial coefficients and their gen...
The Fibonacci numbers are sequences of numbers of the form: 0,1,1,2,3,5,8,13,... Among n...
The Fibonacci numbers are sequences of numbers of the form: 0,1,1,2,3,5,8,13,... Among n...
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