A. F. Horadam
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 3, 1997, Number 3, Pages 117—127
Download full paper: PDF, 328 Kb
Details
Authors and affiliations
A. F. Horadam
University of New England, Armidale, Australia 2351
Abstract
Studying the unique minimal and maximal integer Zeckendorf representations by Pell numbers [2], [3], [4], [5] led to the consideration [6, eqn. (2.7)] of those numbers which are common to both representations, namely, the MinMax numbers. This idea was then carried over to Jacobsthal numbers [7, eqn. (3.1)]. (Earlier, minimal and maximal representations by Fibonacci and Lucas numbers had been investigated in [1].)
Here, the corresponding situation existing for Morgan-Voyce numbers is to be disclosed. Though the results are perhaps not quite so elegant as those for Pell numbers, they are nevertheless of intrinsic interest and value.
AMS Classification
- 11B37
References
- V.E. Hoggatt, Jr. Fibonacci and Lucas Numbers. Houghton Mifflin (1969).
- A.F. Horadam. “Zeckendorf Representations of Positive and Negative Integers by Pell Numbers.” Applications of Fibonacci Numbers, Vol.5 (ed. G.E. Bergum, A.N. Philippou, and A.F. Horadam), Kluwer Academic Publications, Dordrecht (1993): 305-316.
- A.F. Horadam. “Unique Minimal Representation of Integers by Negatively Subscripted Pell Numbers.” The Fibonacci Quarterly 32.3 (1994) 202-206.
- A.F. Horadam. “Maximal Representations of Positive Integers by Pell Numbers.” The Fibonacci Quarterly 32.3 (1994): 240-244.
- A.F. Horadam. “An Alternative Proof of a Unique Representation Theorem.” The Fibonacci Quarterly 32.5 (1994): 409-411.
- A.F. Horadam. “MinMax Sequences for Pell Numbers.” Applications of Fibonacci Numbers, Vol.6 (ed. G.E. Bergum, A.N. Philippou and A.F. Horadam), Kluwer Academic Publications, Dordrecht (1996): 231-249.
- A.F. Horadam. “Jacobsthal Representation Numbers.” The Fibonacci Quarterly 34.1 (1996): 40-54.
- A.F. Horadam. “New Aspects of Morgan-Voyce Polynomials.” (To appear in the proceedings of the Seventh International Conference on Fibonacci Numbers and Their Applications.)
- A.M. Morgan-Voyce. “Ladder Networks Analysis Using Fibonacci Numbers.” I.R.E. Trans. Circuit Theory 6.3 (1959): 321-322.
- N.N. Vorob’ev. Fibonacci Numbers. Pergamon (1961).
Related papers
Cite this paper
Horadam, A. F. (1997). Unit coefficient sums for certain Morgan-Voyce numbers. Notes on Number Theory and Discrete Mathematics, 3(3), 117-127.