On a Sequence of Tridiagonal Matrices, Whose Permanents Are Related to Fibonacci and Lucas Numbers

Abstract

In this paper, we generalize result on connection permanents of special tridiagonal matrices with Fibonacci numbers, as we show that more general sequences of tridiagonal matrices is related to the sequence of Fibonacci numbers.

Recursive and combinational formulas for permanents of general k-tridiagonal Toeplitz matrices

“…In [22], for the permanent of general 2 − tridia onal Toeplitz matrix, two distinct recursive formulas which are separated according to the order of the matrix have been given. In [23][24][25], the permanents of various special tridia onal matrices have been studied. The common feature of these studies is that both the elements used in the matrices are selected from the well-known number sequences, such as Fibonacci and Lucas, and the results obtained are also associated with number sequences.…”

Relationships between the permanents of a certain type of k-tridiagonal symmetric Toeplitz matrix and the Chebyshev polynomials

“…Jina and Trojovsky [9] presented new results about the relationships between the permanents of some tridiagonal matrices and the Fibonacci numbers. Matousova and Trojovsky [10] showed a generalization for sequences of tridiagonal matrices which is related to the sequence of Fibonacci numbers. Kaygısız and Sahin [11] obtained the permanents of some tridiagonal matrices with complex elements in terms of k sequences of generalized order-k Fibonacci numbers.…”

On Determinants of Tridiagonal Matrices With Alternating Pairs of 1' and -1' on the Diagonal Connected With Fibonacci Numbers

“…Many authors derived the similar types of matrices which determinants or permanents are related to Fibonacci numbers or different kinds of their generalizations, e. g. k-generalized Fibonacci numbers, see [5], [7] [2], [6], [9] and [11]. Now we turn our attention to the relation of determinants of special tridiagonal matrices with Fibonacci numbers.…”