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The Dying Rabbit Problem Revisited
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Antonio M. Oller-Marcén
Published/Copyright:
June 15, 2009
Abstract
In this paper we study a generalization of the Fibonacci sequence in which rabbits are mortal and take more that two months to become mature. In particular we give a general recurrence relation for these sequences (improving the work in [Hoggat and Lind, Fibonacci Quart. 7: 482–487, 1969]) and we calculate explicitly their general term (extending the work in [Miles, Amer. Math. Monthly 67: 745–752, 1960]). In passing, and as a technical requirement, we also study the behavior of the positive real roots of the characteristic polynomial of the considered sequences.
Keywords.: Fibonacci sequence; dying rabbit sequence
Received: 2008-01-11
Revised: 2009-02-04
Accepted: 2009-02-25
Published Online: 2009-06-15
Published in Print: 2009-June
© de Gruyter 2009
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- Symmetric Numerical Semigroups Generated by Fibonacci and Lucas Triples
- On Newman's Conjecture and Prime Trees
- The Dying Rabbit Problem Revisited
- A Note on the q-Binomial Rational Root Theorem
- The 3x + 1 Conjugacy Map over a Sturmian Word
- The Number of Relatively Prime Subsets of {1, 2, . . . , n}
- Generalized Levinson–Durbin Sequences and Binomial Coefficients
- Neither (4k2 + 1) nor (2k(k – 1) + 1) is a Perfect Square
- Some Arithmetic Properties of Overpartition k-Tuples
- Characterizations of Midy's Property
Articles in the same Issue
- Symmetric Numerical Semigroups Generated by Fibonacci and Lucas Triples
- On Newman's Conjecture and Prime Trees
- The Dying Rabbit Problem Revisited
- A Note on the q-Binomial Rational Root Theorem
- The 3x + 1 Conjugacy Map over a Sturmian Word
- The Number of Relatively Prime Subsets of {1, 2, . . . , n}
- Generalized Levinson–Durbin Sequences and Binomial Coefficients
- Neither (4k2 + 1) nor (2k(k – 1) + 1) is a Perfect Square
- Some Arithmetic Properties of Overpartition k-Tuples
- Characterizations of Midy's Property
