Unit coefficient sums for certain Morgan-Voyce numbers

A. F. Horadam
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 3, 1997, Number 3, Pages 117–127
Full paper (PDF, 328 Kb)

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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

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2. 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.
3. A.F. Horadam. “Unique Minimal Representation of Integers by Negatively Subscripted Pell Numbers.” The Fibonacci Quarterly 32.3 (1994) 202-206.
4. A.F. Horadam. “Maximal Representations of Positive Integers by Pell Numbers.” The Fibonacci Quarterly 32.3 (1994): 240-244.
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