Circulants and the factorization of the Fibonacci–like numbers

Jaroslav Seibert; Pavel Trojovský

Acta Mathematica Universitatis Ostraviensis (2006)

  • Volume: 14, Issue: 1, page 63-70
  • ISSN: 1804-1388

Abstract

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Several authors gave various factorizations of the Fibonacci and Lucas numbers. The relations are derived with the help of connections between determinants of tridiagonal matrices and the Fibonacci and Lucas numbers using the Chebyshev polynomials. In this paper some results on factorizations of the Fibonacci–like numbers U n and their squares are given. We find the factorizations using the circulant matrices, their determinants and eigenvalues.

How to cite

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Seibert, Jaroslav, and Trojovský, Pavel. "Circulants and the factorization of the Fibonacci–like numbers." Acta Mathematica Universitatis Ostraviensis 14.1 (2006): 63-70. <http://eudml.org/doc/35164>.

@article{Seibert2006,
abstract = {Several authors gave various factorizations of the Fibonacci and Lucas numbers. The relations are derived with the help of connections between determinants of tridiagonal matrices and the Fibonacci and Lucas numbers using the Chebyshev polynomials. In this paper some results on factorizations of the Fibonacci–like numbers $U_n$ and their squares are given. We find the factorizations using the circulant matrices, their determinants and eigenvalues.},
author = {Seibert, Jaroslav, Trojovský, Pavel},
journal = {Acta Mathematica Universitatis Ostraviensis},
keywords = {Fibonacci and Lucas numbers; tridiagonal matrix; circulant; Fibonacci-like numbers; factorization},
language = {eng},
number = {1},
pages = {63-70},
publisher = {University of Ostrava},
title = {Circulants and the factorization of the Fibonacci–like numbers},
url = {http://eudml.org/doc/35164},
volume = {14},
year = {2006},
}

TY - JOUR
AU - Seibert, Jaroslav
AU - Trojovský, Pavel
TI - Circulants and the factorization of the Fibonacci–like numbers
JO - Acta Mathematica Universitatis Ostraviensis
PY - 2006
PB - University of Ostrava
VL - 14
IS - 1
SP - 63
EP - 70
AB - Several authors gave various factorizations of the Fibonacci and Lucas numbers. The relations are derived with the help of connections between determinants of tridiagonal matrices and the Fibonacci and Lucas numbers using the Chebyshev polynomials. In this paper some results on factorizations of the Fibonacci–like numbers $U_n$ and their squares are given. We find the factorizations using the circulant matrices, their determinants and eigenvalues.
LA - eng
KW - Fibonacci and Lucas numbers; tridiagonal matrix; circulant; Fibonacci-like numbers; factorization
UR - http://eudml.org/doc/35164
ER -

References

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  1. Fibonacci determinants, College Mathematics Journal 33.3 (2002), 221-225. (2002) 
  2. Complex factorizations of the Fibonacci and Lucas numbers, The Fibonacci Quarterly 41.1 (2003), 13-19. (2003) MR1962276
  3. Fibonacci and Lucas numbers as tridiagonal matrix determinants, The Fibonacci Quarterly 42.2 (2004), 216-221. (2004) MR2093876
  4. Tables of Integrals, Series and Products, 5th ed. San Diego, CA: Academic Press, 1979. (1979) 
  5. Elliptic functions and Lambert series in the summation of reciprocals in certain recurrence–generated sequences, The Fibonacci Quarterly 26.2 (1988), 98-114. (1988) Zbl0647.10014MR0938583

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