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Article overview
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Asymptotics of Lagged Fibonacci Sequences | Stephan Mertens
; Stefan Boettcher
; | Date: |
12 Dec 2009 | Abstract: | Consider "lagged" Fibonacci sequences $a(n) = a(n-1)+a(lfloor n/k
floor)$
for $k > 1$. We show that $lim_{n oinfty} a(kn)/a(n)cdotln n/n = kln k$
and we demonstrate the slow numerical convergence to this limit and how to deal
with this slow convergence. We also discuss the connection between two
classical results of N.G. de Bruijn and K. Mahler on the asymptotics of $a(n)$. | Source: | arXiv, 0912.2459 | Services: | Forum | Review | PDF | Favorites |
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