[seqfan] Re: estimating growth of a sequence

Robert Israel israel at math.ubc.ca
Wed Apr 6 21:07:36 CEST 2011

Hmm.  It looks to me like a(n)/4^n * n * ln(n)^2 is decreasing for n > 61, 
so I might guess something more like a(n) ~ c * 4^n/(n*ln(n)^2), where
0 <= c < 0.84.  But with so few data points, trying to guess these 
logarithmic factors is very tricky.

Robert Israel                                israel at math.ubc.ca
Department of Mathematics        http://www.math.ubc.ca/~israel 
University of British Columbia            Vancouver, BC, Canada

On Wed, 6 Apr 2011, N. J. A. Sloane wrote:

> Dear Sequence Fans, This is a problem that I encounter
> all the time. I have 120 terms of a sequence,
> and I want a good guess for the asymptotic rate of growth.
> My current problem is A156043. I created a b-file of 120 terms.
> Very crudely it seems that
> a(n) is approaching 4^n / ( 6 n ln n).
> But I don't have much confidence in that.
> Is there a package in Maple or some other language that will do this sort
> of thing automatically?
> Statisticians must need this.
> Neil
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