Consider the Fibonacci sequence {Fn}n=0 having initial conditions F0 = 0, F1 = 1 and recurrence relation Fn = Fn−1 + Fn−2 (n ≥ 2). The Fibonacci sequence has been generalized in many ways, some by preserving the initial conditions, and others by preserving the recurrence relation. In this article, we study a new generalization {qn}, with initial conditions q0 = 0 and q1 = 1 which is generated b...

In this paper, we introduce a tiling approach to (p,q)-Fibonacci and (p,q)-Lucas numbers that generalize of the well-known Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal ve Jacobsthal-Lucas numbers. We show nth number is interpreted as ways tile 1×n board with cells labeled 1,2,...,n using colored 1×1 squares 1×2 dominoes, where there are p kind colors for q dominoes. Then circular also present...

Consider the Fibonacci sequence {Fn}n=0 with initial conditions F0 = 0, F1 = 1 and recurrence relation Fn = Fn−1 + Fn−2 (n ≥ 2). The Fibonacci sequence has been generalized in many ways, some by preserving the initial conditions, and others by preserving the recurrence relation. In this article, we study a new generalization {qn}, with initial conditions q0 = 0 and q1 = 1, which is generated by...

In this paper, we define bi-periodic (p,q)-Fibonacci and (p,q)-Lucas sequences, which generalize Fibonacci type, Lucas type using recurrence relations of sequences. Generating functions Binet formulas that allow us to calculate the nth terms these sequences are given convergence properties their consecutive examined. Also, prove some fundamental identities conform well-known

In this study, by using Fibonacci Q-matrix and Lucas Q^'-matrix we define bicomplex Q^'-matrix. After that matrix representation, give some identities.

We give several identities about Fibonacci and Lucas hybrid numbers. introduce the numbers with negative subscripts. obtain different Cassini for conjugate of by two determinant definitions a square matrix (whose entries are numbers).