# The Fibonacci decomposition of symmetric Tetranacci polynomials

@inproceedings{Leumer2022TheFD, title={The Fibonacci decomposition of symmetric Tetranacci polynomials}, author={Nico Leumer}, year={2022} }

. In this manuscript, we introduce (symmetric) Tetranacci polynomials ξ j as a twofold generalization of ordinary Tetranacci numbers, by considering both non unity coeﬃcients and generic initial values in their recursive deﬁnition. The issue of these polynomials arose in condensed matter physics and the diagonalization of symmetric Toeplitz matrices having in total four non-zero oﬀ diagonals. For the latter, the symmetric Tetranacci polynomials are the basic entities of the associated…

## References

SHOWING 1-10 OF 32 REFERENCES

### DIVISIBILITY PROPERTIES OF GENERALIZED FIBONACCI POLYNOMIALS

- Mathematics
- 2010

As one would expect, these polynomials possess many properties of the Fibonacci sequence which, of course, is just the integral sequence {f (1)}. However, a most surprising result is that f (x) is…

### EIGENVALUES AND EIGENVECTORS OF TRIDIAGONAL MATRICES

- Mathematics
- 2006

This paper is continuation of previous work by the present author, where explicit formulas for the eigenvalues associated with several tridiagonal matrices were given. In this paper the associated…

### Binet – Type Formula For The Sequence of Tetranacci Numbers by Alternate Methods

- MathematicsMathematical Journal of Interdisciplinary Sciences
- 2019

The sequence {Tn} of Tetranacci numbers is defined by recurrence relation Tn= Tn-1 + Tn-2 + Tn-3 + Tn-4; n≥4 with initial condition T0=T1=T2=0 and T3=1. In this Paper, we obtain the explicit…

### An Another Generalized Fibonacci Sequence

- Mathematics
- 2017

where C = C ' + C . n > 3, with C1 = C2 = 1 . n n-i n-2 * l Some recent generalizations have produced a variety of new and extended results. „ A search of the literature seems to reveal that efforts…

### More Identities On The Tribonacci Numbers

- MathematicsArs Comb.
- 2011

In this paper, a simple method is used to derive di¤erent recurrence relations on the Tribonacci numbers and their sums by using the companion matrices and generating matrices, which are more general than that given in literature.

### Gaussian Tetranacci Numbers

- Mathematics, Computer Science
- 2017

Gaussian Tetranacci sequence is defined, generating function, Binet-like formula, sum formulas and matrix representation of Gaussian tetranacci numbers are given, and the latter are given in detail.

### Generalized Fibonacci Sequences and Binet-Fibonacci Curves

- Mathematics
- 2017

We have studied several generalizations of Fibonacci sequences as the sequences with arbitrary initial values, the addition of two and more Fibonacci subsequences and Fibonacci polynomials with…

### A formula for Eigenpairs of certain symmetric tridiagonal matrices

- MathematicsBulletin of the Australian Mathematical Society
- 1997

A closed form expression is given for the eigenvalues and eigenvectors of a symmetric tridiagonal matrix of odd order whose diagonal elements are all equal and whoes superdiagonal elements alternate…