2007/10/11 by Antonio M. Oller‐Marcén, Oller, Antonio M. · 1 citation
Physics and Astronomy · #Quantum Mechanics and Applications #Advanced Thermodynamics and Statistical Mechanics
paper · pdf · doi:10.48550/arxiv.0710.2216
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.