Let 1, 2, 3, 5, 8, … denote the Fibonacci sequence beginning with 1 and 2, and then setting each subsequent number to the sum of the two previous ones. Every positive integer n can be expressed as a sum of distinct Fibonacci numbers in one or more ways. Setting R(n) to be the number of ways n can be written as a sum of distinct Fibonacci numbers, we exhibit certain regularity properties of R(n), one of which is connected to the Euler φ-function. In addition, using a theorem of Fine and Wilf, we give a formula for R(n) in terms of binomial coefficients modulo two.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc3676 |
| Date | 05 1900 |
| Creators | Edson, Marcia Ruth |
| Contributors | Zamboni, Luca, Cherry, William, 1966-, Richter, Olav |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | Text |
| Rights | Public, Copyright, Edson, Marcia Ruth, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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