Fibonacci Facts and Formulas

R. M. Capocelli, G. Cerbone, P. Cull and J. L. Holloway
Additional contact information
R. M. Capocelli: Universita’ di Salerno, Dipartimento di Informatica ed Applocazioni
G. Cerbone: Oregon State University, Department of Computer Science
P. Cull: Oregon State University, Department of Computer Science
J. L. Holloway: Oregon State University, Department of Computer Science

A chapter in Sequences, 1990, pp 123-137 from Springer

Abstract: Abstract We investigate several methods of computing Fibonacci numbers quickly and generalize some properties of the Fibonacci numbers to degree r Fibonacci (R-nacci) numbers. Sections 2 and 3 present several algorithms for computing the traditional, degree two, Fibonacci numbers quickly. Sections 4 and 5 investigate the structure of the binary representation of the Fibonacci numbers. Section 6 shows how the generalized Fibonacci numbers can be expressed as rounded powers of the dominant root of the characteristic equation. Properties of the roots of the characteristic equation of the generalized Fibonacci numbers are presented in Section 7. Section 8 introduces several properties of the Zeckendorf representation of the integers. Finally, in Section 9 the asymptotic proportion of l’s in the Zeckendorf representation of integers is computed and an easy to compute closed formula is given.

Keywords: Binary Sequence; Compression Algorithm; Binary Representation; Fibonacci Number; Fibonacci Sequence (search for similar items in EconPapers)
Date: 1990
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-3352-7_9

Ordering information: This item can be ordered from
http://www.springer.com/9781461233527

DOI: 10.1007/978-1-4612-3352-7_9

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().