# The dying rabbit problem revisited

- Published in 2007
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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 the paper Hoggatt, V. E., Jr.; Lind, D. A. "The dying rabbit problem". Fibonacci Quart. 7 1969 no. 5, 482--487) and we calculate explicitly their general term (extending the work in the paper Miles, E. P., Jr. Generalized Fibonacci numbers and associated matrices. Amer. Math. Monthly 67 1960 745--752). 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.

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- 8

### BibTeX entry

@article{Oller2007, 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 the paper Hoggatt, V. E., Jr.; Lind, D. A. "The dying rabbit problem". Fibonacci Quart. 7 1969 no. 5, 482--487) and we calculate explicitly their general term (extending the work in the paper Miles, E. P., Jr. Generalized Fibonacci numbers and associated matrices. Amer. Math. Monthly 67 1960 745--752). 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.}, author = {Oller, Antonio M.}, month = {oct}, pages = 8, title = {The dying rabbit problem revisited}, url = {http://arxiv.org/abs/0710.2216 http://arxiv.org/pdf/0710.2216v1}, year = 2007, archivePrefix = {arXiv}, eprint = {0710.2216}, primaryClass = {math.NT}, urldate = {2015-02-18}, collections = {Easily explained,Animals,Fibonaccinalia} }