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Sequences defined as minima of two Fibonacci-type relations
Published online by Cambridge University Press: 17 April 2009
Abstract
If {Ln} is a sequence defined by Ln = min {Ln-a +Ln-b, Ln-c +Ln-d}, with a, b, c, d positive integers, then one can ask if necessarily Ln = Ln-b + Ln-b, for all sufficiently large n.
The answer is yes if a and b are relatively prime, Ln > 0 initially, and λ < μ, where λ-a + λ-b = 1, μ-c + μ-d = 1. The answer is no if instead a and b have greatest common divisor k ≥2, with c ≡ 0 (mod k), d ≢ 0 (mod k).
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- Copyright © Australian Mathematical Society 1972
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